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The dataset generation failed
Error code: DatasetGenerationError
Exception: ArrowInvalid
Message: JSON parse error: Invalid value. in row 0
Traceback: Traceback (most recent call last):
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/packaged_modules/json/json.py", line 160, in _generate_tables
df = pandas_read_json(f)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/packaged_modules/json/json.py", line 38, in pandas_read_json
return pd.read_json(path_or_buf, **kwargs)
File "/src/services/worker/.venv/lib/python3.9/site-packages/pandas/io/json/_json.py", line 791, in read_json
json_reader = JsonReader(
File "/src/services/worker/.venv/lib/python3.9/site-packages/pandas/io/json/_json.py", line 905, in __init__
self.data = self._preprocess_data(data)
File "/src/services/worker/.venv/lib/python3.9/site-packages/pandas/io/json/_json.py", line 917, in _preprocess_data
data = data.read()
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/utils/file_utils.py", line 827, in read_with_retries
out = read(*args, **kwargs)
File "/usr/local/lib/python3.9/codecs.py", line 322, in decode
(result, consumed) = self._buffer_decode(data, self.errors, final)
UnicodeDecodeError: 'utf-8' codec can't decode byte 0x89 in position 0: invalid start byte
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1855, in _prepare_split_single
for _, table in generator:
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/packaged_modules/json/json.py", line 163, in _generate_tables
raise e
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/packaged_modules/json/json.py", line 137, in _generate_tables
pa_table = paj.read_json(
File "pyarrow/_json.pyx", line 308, in pyarrow._json.read_json
File "pyarrow/error.pxi", line 154, in pyarrow.lib.pyarrow_internal_check_status
File "pyarrow/error.pxi", line 91, in pyarrow.lib.check_status
pyarrow.lib.ArrowInvalid: JSON parse error: Invalid value. in row 0
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1433, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1050, in convert_to_parquet
builder.download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 925, in download_and_prepare
self._download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1001, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1742, in _prepare_split
for job_id, done, content in self._prepare_split_single(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1898, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
data_id
string | image
string | state
string | plot_level
string | qa_type
string | qa_level
string | question_id
int64 | question_description
string | question
string | answer
string | options
sequence | analysis
string | game_name
string | game_type
string | plot_id
null | Options
null |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
turing-machine-test-00001 | games_images_test/2d_turing_machine/00001.png | states/00001.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move up, New State 1
State 0, Symbol 1 -> Write 2, Move up, New State 1
State 0, Symbol 2 -> Write 2, Move right, New State 1
State 0, Symbol 3 -> Write 0, Move up, New State 1
State 1, Symbol 0 -> Write 2, Move right, New State 0
State 1, Symbol 1 -> Write 1, Move down, New State 1
State 1, Symbol 2 -> Write 1, Move down, New State 2
State 1, Symbol 3 -> Write 2, Move up, New State 1
State 2, Symbol 0 -> Write 1, Move left, New State 2
State 2, Symbol 1 -> Write 3, Move up, New State 0
State 2, Symbol 2 -> Write 3, Move up, New State 0
State 2, Symbol 3 -> Write 3, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 0) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 4 steps?
Options:
1: (1, 0)
2: (0, 0)
3: (0, 2)
4: (2, 2)
5: (1, 2)
6: (1, 1)
7: (2, 1)
8: (0, 1)
| 1 | [
"(1, 0)",
"(0, 0)",
"(0, 2)",
"(2, 2)",
"(1, 2)",
"(1, 1)",
"(2, 1)",
"(0, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move up, New State 1
- **Symbol Written on (1, 0):** 2
- **New Position:** (0, 0)
- **New State:** 1
Step 2:
- **Position:** (0, 0)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move down, New State 1
- **Symbol Written on (0, 0):** 1
- **New Position:** (1, 0)
- **New State:** 1
Step 3:
- **Position:** (1, 0)
- **State:** 1
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: [2]
- **Action:** Write 1, Move down, New State 2
- **Symbol Written on (1, 0):** 1
- **New Position:** (2, 0)
- **New State:** 2
Step 4:
- **Position:** (2, 0)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 3, Move up, New State 0
- **Symbol Written on (2, 0):** 3
- **New Position:** (1, 0)
- **New State:** 0
Therefore, the final position after 4 steps will be (1, 0).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00002 | games_images_test/2d_turing_machine/00002.png | states/00002.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move left, New State 2
State 0, Symbol 1 -> Write 1, Move up, New State 0
State 0, Symbol 2 -> Write 2, Move right, New State 2
State 1, Symbol 0 -> Write 1, Move up, New State 2
State 1, Symbol 1 -> Write 2, Move right, New State 3
State 1, Symbol 2 -> Write 0, Move up, New State 3
State 2, Symbol 0 -> Write 0, Move up, New State 3
State 2, Symbol 1 -> Write 1, Move down, New State 0
State 2, Symbol 2 -> Write 2, Move down, New State 3
State 3, Symbol 0 -> Write 0, Move down, New State 2
State 3, Symbol 1 -> Write 0, Move up, New State 1
State 3, Symbol 2 -> Write 0, Move left, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (4, 2) with State 1 on Symbol 2 that is [2].
Question: where will the head be after 5 steps?
Options:
1: (0, 1)
2: (1, 2)
3: (4, 1)
4: (3, 1)
5: (1, 1)
6: (3, 2)
7: (1, 0)
8: (2, 0)
| 6 | [
"(0, 1)",
"(1, 2)",
"(4, 1)",
"(3, 1)",
"(1, 1)",
"(3, 2)",
"(1, 0)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (4, 2)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 0, Move up, New State 3
- **Symbol Written on (4, 2):** 0
- **New Position:** (3, 2)
- **New State:** 3
Step 2:
- **Position:** (3, 2)
- **State:** 3
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: <2>
- **Action:** Write 0, Move left, New State 2
- **Symbol Written on (3, 2):** 0
- **New Position:** (3, 1)
- **New State:** 2
Step 3:
- **Position:** (3, 1)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (3, 1):** 1
- **New Position:** (4, 1)
- **New State:** 0
Step 4:
- **Position:** (4, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move right, New State 2
- **Symbol Written on (4, 1):** 2
- **New Position:** (4, 2)
- **New State:** 2
Step 5:
- **Position:** (4, 2)
- **State:** 2
- **Symbol:** According to step 1, it has been changed to symbol 0
- **State and Symbol**: {0}
- **Action:** Write 0, Move up, New State 3
- **Symbol Written on (4, 2):** 0
- **New Position:** (3, 2)
- **New State:** 3
Therefore, the final position after 5 steps will be (3, 2).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00003 | games_images_test/2d_turing_machine/00003.png | states/00003.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move right, New State 1
State 0, Symbol 1 -> Write 3, Move down, New State 0
State 0, Symbol 2 -> Write 1, Move left, New State 1
State 0, Symbol 3 -> Write 3, Move up, New State 2
State 1, Symbol 0 -> Write 3, Move left, New State 1
State 1, Symbol 1 -> Write 1, Move up, New State 1
State 1, Symbol 2 -> Write 3, Move up, New State 0
State 1, Symbol 3 -> Write 3, Move down, New State 0
State 2, Symbol 0 -> Write 3, Move left, New State 0
State 2, Symbol 1 -> Write 1, Move left, New State 0
State 2, Symbol 2 -> Write 1, Move left, New State 2
State 2, Symbol 3 -> Write 3, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 3) with State 1 on Symbol 2 that is [2].
Question: where will the head be after 4 steps?
Options:
1: (0, 1)
2: (3, 0)
3: (2, 2)
4: (0, 3)
5: (3, 1)
6: (0, 0)
7: (2, 3)
8: (2, 0)
| 1 | [
"(0, 1)",
"(3, 0)",
"(2, 2)",
"(0, 3)",
"(3, 1)",
"(0, 0)",
"(2, 3)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 3)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 3, Move up, New State 0
- **Symbol Written on (2, 3):** 3
- **New Position:** (1, 3)
- **New State:** 0
Step 2:
- **Position:** (1, 3)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move up, New State 2
- **Symbol Written on (1, 3):** 3
- **New Position:** (0, 3)
- **New State:** 2
Step 3:
- **Position:** (0, 3)
- **State:** 2
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: {2}
- **Action:** Write 1, Move left, New State 2
- **Symbol Written on (0, 3):** 1
- **New Position:** (0, 2)
- **New State:** 2
Step 4:
- **Position:** (0, 2)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 3, Move left, New State 0
- **Symbol Written on (0, 2):** 3
- **New Position:** (0, 1)
- **New State:** 0
Therefore, the final position after 4 steps will be (0, 1).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00004 | games_images_test/2d_turing_machine/00004.png | states/00004.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move up, New State 1
State 0, Symbol 1 -> Write 0, Move left, New State 1
State 0, Symbol 2 -> Write 1, Move down, New State 0
State 0, Symbol 3 -> Write 1, Move right, New State 1
State 1, Symbol 0 -> Write 2, Move right, New State 0
State 1, Symbol 1 -> Write 2, Move up, New State 0
State 1, Symbol 2 -> Write 1, Move up, New State 0
State 1, Symbol 3 -> Write 1, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 1) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 3 steps?
Options:
1: (3, 0)
2: (2, 2)
3: (1, 2)
4: (4, 0)
5: (2, 1)
6: (0, 2)
7: (4, 2)
8: (0, 1)
| 5 | [
"(3, 0)",
"(2, 2)",
"(1, 2)",
"(4, 0)",
"(2, 1)",
"(0, 2)",
"(4, 2)",
"(0, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move up, New State 1
- **Symbol Written on (3, 1):** 0
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (2, 1):** 2
- **New Position:** (1, 1)
- **New State:** 0
Step 3:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (1, 1):** 1
- **New Position:** (2, 1)
- **New State:** 0
Therefore, the final position after 3 steps will be (2, 1).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00005 | games_images_test/2d_turing_machine/00005.png | states/00005.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move right, New State 1
State 0, Symbol 1 -> Write 1, Move right, New State 3
State 0, Symbol 2 -> Write 0, Move up, New State 0
State 1, Symbol 0 -> Write 2, Move down, New State 3
State 1, Symbol 1 -> Write 2, Move up, New State 3
State 1, Symbol 2 -> Write 0, Move left, New State 2
State 2, Symbol 0 -> Write 0, Move down, New State 0
State 2, Symbol 1 -> Write 1, Move left, New State 2
State 2, Symbol 2 -> Write 0, Move down, New State 0
State 3, Symbol 0 -> Write 0, Move down, New State 1
State 3, Symbol 1 -> Write 2, Move left, New State 1
State 3, Symbol 2 -> Write 2, Move up, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 0) with State 2 on Symbol 2 that is {2}.
Question: where will the head be after 5 steps?
Options:
1: (2, 1)
2: (3, 1)
3: (1, 2)
4: (3, 2)
5: (0, 0)
6: (1, 1)
7: (3, 0)
8: (1, 0)
| 1 | [
"(2, 1)",
"(3, 1)",
"(1, 2)",
"(3, 2)",
"(0, 0)",
"(1, 1)",
"(3, 0)",
"(1, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 0)
- **State:** 2
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: {2}
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (0, 0):** 0
- **New Position:** (1, 0)
- **New State:** 0
Step 2:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (1, 0):** 0
- **New Position:** (0, 0)
- **New State:** 0
Step 3:
- **Position:** (0, 0)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (0, 0):** 2
- **New Position:** (0, 1)
- **New State:** 1
Step 4:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 2, Move down, New State 3
- **Symbol Written on (0, 1):** 2
- **New Position:** (1, 1)
- **New State:** 3
Step 5:
- **Position:** (1, 1)
- **State:** 3
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: <0>
- **Action:** Write 0, Move down, New State 1
- **Symbol Written on (1, 1):** 0
- **New Position:** (2, 1)
- **New State:** 1
Therefore, the final position after 5 steps will be (2, 1).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00006 | games_images_test/2d_turing_machine/00006.png | states/00006.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move right, New State 1
State 0, Symbol 1 -> Write 3, Move right, New State 1
State 0, Symbol 2 -> Write 2, Move down, New State 1
State 0, Symbol 3 -> Write 0, Move down, New State 0
State 1, Symbol 0 -> Write 1, Move up, New State 0
State 1, Symbol 1 -> Write 0, Move up, New State 1
State 1, Symbol 2 -> Write 3, Move down, New State 0
State 1, Symbol 3 -> Write 3, Move left, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (1, 1) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 4 steps?
Options:
1: (3, 0)
2: (2, 0)
3: (4, 2)
4: (4, 4)
5: (2, 2)
6: (2, 4)
7: (3, 4)
8: (1, 2)
| 5 | [
"(3, 0)",
"(2, 0)",
"(4, 2)",
"(4, 4)",
"(2, 2)",
"(2, 4)",
"(3, 4)",
"(1, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 3, Move right, New State 1
- **Symbol Written on (1, 1):** 3
- **New Position:** (1, 2)
- **New State:** 1
Step 2:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 3, Move left, New State 0
- **Symbol Written on (1, 2):** 3
- **New Position:** (1, 1)
- **New State:** 0
Step 3:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (1, 1):** 0
- **New Position:** (2, 1)
- **New State:** 0
Step 4:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move right, New State 1
- **Symbol Written on (2, 1):** 0
- **New Position:** (2, 2)
- **New State:** 1
Therefore, the final position after 4 steps will be (2, 2).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00007 | games_images_test/2d_turing_machine/00007.png | states/00007.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move left, New State 0
State 0, Symbol 1 -> Write 2, Move up, New State 0
State 0, Symbol 2 -> Write 1, Move down, New State 0
State 1, Symbol 0 -> Write 0, Move left, New State 0
State 1, Symbol 1 -> Write 1, Move left, New State 1
State 1, Symbol 2 -> Write 0, Move down, New State 0
State 2, Symbol 0 -> Write 2, Move left, New State 0
State 2, Symbol 1 -> Write 0, Move left, New State 1
State 2, Symbol 2 -> Write 0, Move down, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 3) with State 1 on Symbol 1 that is [1].
Question: where will the head be after 8 steps?
Options:
1: (3, 3)
2: (4, 2)
3: (1, 1)
4: (3, 0)
5: (4, 1)
6: (4, 0)
7: (2, 4)
8: (0, 2)
| 6 | [
"(3, 3)",
"(4, 2)",
"(1, 1)",
"(3, 0)",
"(4, 1)",
"(4, 0)",
"(2, 4)",
"(0, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 3)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (3, 3):** 1
- **New Position:** (3, 2)
- **New State:** 1
Step 2:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (3, 2):** 1
- **New Position:** (3, 1)
- **New State:** 1
Step 3:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (3, 1):** 0
- **New Position:** (4, 1)
- **New State:** 0
Step 4:
- **Position:** (4, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (4, 1):** 2
- **New Position:** (3, 1)
- **New State:** 0
Step 5:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move left, New State 0
- **Symbol Written on (3, 1):** 0
- **New Position:** (3, 0)
- **New State:** 0
Step 6:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 0):** 2
- **New Position:** (2, 0)
- **New State:** 0
Step 7:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (2, 0):** 1
- **New Position:** (3, 0)
- **New State:** 0
Step 8:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** According to step 6, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (3, 0):** 1
- **New Position:** (4, 0)
- **New State:** 0
Therefore, the final position after 8 steps will be (4, 0).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00008 | games_images_test/2d_turing_machine/00008.png | states/00008.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move down, New State 1
State 0, Symbol 1 -> Write 1, Move right, New State 1
State 0, Symbol 2 -> Write 1, Move right, New State 2
State 1, Symbol 0 -> Write 2, Move right, New State 0
State 1, Symbol 1 -> Write 0, Move up, New State 0
State 1, Symbol 2 -> Write 0, Move up, New State 1
State 2, Symbol 0 -> Write 2, Move left, New State 1
State 2, Symbol 1 -> Write 1, Move right, New State 2
State 2, Symbol 2 -> Write 1, Move up, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 1) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 4 steps?
Options:
1: (4, 2)
2: (2, 0)
3: (1, 2)
4: (3, 1)
5: (3, 2)
6: (0, 1)
7: (0, 2)
8: (4, 1)
| 4 | [
"(4, 2)",
"(2, 0)",
"(1, 2)",
"(3, 1)",
"(3, 2)",
"(0, 1)",
"(0, 2)",
"(4, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (3, 1):** 2
- **New Position:** (4, 1)
- **New State:** 1
Step 2:
- **Position:** (4, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (4, 1):** 0
- **New Position:** (3, 1)
- **New State:** 0
Step 3:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move right, New State 2
- **Symbol Written on (3, 1):** 1
- **New Position:** (3, 2)
- **New State:** 2
Step 4:
- **Position:** (3, 2)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 2, Move left, New State 1
- **Symbol Written on (3, 2):** 2
- **New Position:** (3, 1)
- **New State:** 1
Therefore, the final position after 4 steps will be (3, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00009 | games_images_test/2d_turing_machine/00009.png | states/00009.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move right, New State 0
State 0, Symbol 1 -> Write 3, Move up, New State 0
State 0, Symbol 2 -> Write 0, Move left, New State 1
State 0, Symbol 3 -> Write 0, Move down, New State 0
State 0, Symbol 4 -> Write 3, Move left, New State 0
State 1, Symbol 0 -> Write 2, Move left, New State 0
State 1, Symbol 1 -> Write 3, Move up, New State 0
State 1, Symbol 2 -> Write 1, Move right, New State 1
State 1, Symbol 3 -> Write 1, Move up, New State 0
State 1, Symbol 4 -> Write 0, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (2, 2) with State 0 on Symbol 4 that is (4).
Question: where will the head be after 6 steps?
Options:
1: (0, 0)
2: (3, 2)
3: (0, 1)
4: (0, 2)
5: (2, 2)
6: (2, 0)
7: (3, 1)
8: (2, 1)
| 6 | [
"(0, 0)",
"(3, 2)",
"(0, 1)",
"(0, 2)",
"(2, 2)",
"(2, 0)",
"(3, 1)",
"(2, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: (4)
- **Action:** Write 3, Move left, New State 0
- **Symbol Written on (2, 2):** 3
- **New Position:** (2, 1)
- **New State:** 0
Step 2:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move left, New State 1
- **Symbol Written on (2, 1):** 0
- **New Position:** (2, 0)
- **New State:** 1
Step 3:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (2, 0):** 1
- **New Position:** (1, 0)
- **New State:** 0
Step 4:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 3, Move up, New State 0
- **Symbol Written on (1, 0):** 3
- **New Position:** (0, 0)
- **New State:** 0
Step 5:
- **Position:** (0, 0)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (0, 0):** 0
- **New Position:** (1, 0)
- **New State:** 0
Step 6:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** According to step 4, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (1, 0):** 0
- **New Position:** (2, 0)
- **New State:** 0
Therefore, the final position after 6 steps will be (2, 0).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00010 | games_images_test/2d_turing_machine/00010.png | states/00010.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move right, New State 1
State 0, Symbol 1 -> Write 3, Move left, New State 2
State 0, Symbol 2 -> Write 0, Move up, New State 0
State 0, Symbol 3 -> Write 2, Move left, New State 2
State 1, Symbol 0 -> Write 1, Move right, New State 1
State 1, Symbol 1 -> Write 1, Move left, New State 0
State 1, Symbol 2 -> Write 3, Move down, New State 0
State 1, Symbol 3 -> Write 2, Move left, New State 1
State 2, Symbol 0 -> Write 1, Move right, New State 1
State 2, Symbol 1 -> Write 3, Move down, New State 2
State 2, Symbol 2 -> Write 1, Move left, New State 0
State 2, Symbol 3 -> Write 3, Move down, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 2) with State 1 on Symbol 3 that is [3].
Question: where will the head be after 8 steps?
Options:
1: (3, 1)
2: (0, 2)
3: (0, 1)
4: (3, 2)
5: (2, 1)
6: (1, 2)
7: (1, 1)
8: (1, 0)
| 7 | [
"(3, 1)",
"(0, 2)",
"(0, 1)",
"(3, 2)",
"(2, 1)",
"(1, 2)",
"(1, 1)",
"(1, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 2)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 2, Move left, New State 1
- **Symbol Written on (0, 2):** 2
- **New Position:** (0, 1)
- **New State:** 1
Step 2:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 3, Move down, New State 0
- **Symbol Written on (0, 1):** 3
- **New Position:** (1, 1)
- **New State:** 0
Step 3:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (1, 1):** 2
- **New Position:** (1, 2)
- **New State:** 1
Step 4:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move left, New State 0
- **Symbol Written on (1, 2):** 1
- **New Position:** (1, 1)
- **New State:** 0
Step 5:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (1, 1):** 0
- **New Position:** (0, 1)
- **New State:** 0
Step 6:
- **Position:** (0, 1)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 2, Move left, New State 2
- **Symbol Written on (0, 1):** 2
- **New Position:** (0, 0)
- **New State:** 2
Step 7:
- **Position:** (0, 0)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 1, Move right, New State 1
- **Symbol Written on (0, 0):** 1
- **New Position:** (0, 1)
- **New State:** 1
Step 8:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** According to step 6, it has been changed to symbol 2
- **State and Symbol**: [2]
- **Action:** Write 3, Move down, New State 0
- **Symbol Written on (0, 1):** 3
- **New Position:** (1, 1)
- **New State:** 0
Therefore, the final position after 8 steps will be (1, 1).
The answer is option 7. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00011 | games_images_test/2d_turing_machine/00011.png | states/00011.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move up, New State 1
State 0, Symbol 1 -> Write 2, Move right, New State 1
State 0, Symbol 2 -> Write 0, Move down, New State 0
State 0, Symbol 3 -> Write 0, Move right, New State 3
State 1, Symbol 0 -> Write 3, Move down, New State 3
State 1, Symbol 1 -> Write 1, Move right, New State 1
State 1, Symbol 2 -> Write 0, Move up, New State 0
State 1, Symbol 3 -> Write 3, Move right, New State 1
State 2, Symbol 0 -> Write 1, Move left, New State 0
State 2, Symbol 1 -> Write 3, Move down, New State 2
State 2, Symbol 2 -> Write 2, Move left, New State 3
State 2, Symbol 3 -> Write 0, Move up, New State 3
State 3, Symbol 0 -> Write 1, Move up, New State 2
State 3, Symbol 1 -> Write 2, Move left, New State 1
State 3, Symbol 2 -> Write 3, Move left, New State 1
State 3, Symbol 3 -> Write 0, Move right, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 4) with State 3 on Symbol 1 that is <1>.
Question: where will the head be after 8 steps?
Options:
1: (2, 4)
2: (1, 1)
3: (0, 2)
4: (3, 4)
5: (4, 1)
6: (3, 3)
7: (3, 1)
8: (1, 2)
| 6 | [
"(2, 4)",
"(1, 1)",
"(0, 2)",
"(3, 4)",
"(4, 1)",
"(3, 3)",
"(3, 1)",
"(1, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 4)
- **State:** 3
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: <1>
- **Action:** Write 2, Move left, New State 1
- **Symbol Written on (2, 4):** 2
- **New Position:** (2, 3)
- **New State:** 1
Step 2:
- **Position:** (2, 3)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 3, Move down, New State 3
- **Symbol Written on (2, 3):** 3
- **New Position:** (3, 3)
- **New State:** 3
Step 3:
- **Position:** (3, 3)
- **State:** 3
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: <1>
- **Action:** Write 2, Move left, New State 1
- **Symbol Written on (3, 3):** 2
- **New Position:** (3, 2)
- **New State:** 1
Step 4:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move right, New State 1
- **Symbol Written on (3, 2):** 1
- **New Position:** (3, 3)
- **New State:** 1
Step 5:
- **Position:** (3, 3)
- **State:** 1
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: [2]
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (3, 3):** 0
- **New Position:** (2, 3)
- **New State:** 0
Step 6:
- **Position:** (2, 3)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 0, Move right, New State 3
- **Symbol Written on (2, 3):** 0
- **New Position:** (2, 4)
- **New State:** 3
Step 7:
- **Position:** (2, 4)
- **State:** 3
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: <2>
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (2, 4):** 3
- **New Position:** (2, 3)
- **New State:** 1
Step 8:
- **Position:** (2, 3)
- **State:** 1
- **Symbol:** According to step 6, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 3, Move down, New State 3
- **Symbol Written on (2, 3):** 3
- **New Position:** (3, 3)
- **New State:** 3
Therefore, the final position after 8 steps will be (3, 3).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00012 | games_images_test/2d_turing_machine/00012.png | states/00012.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move up, New State 0
State 0, Symbol 1 -> Write 2, Move right, New State 2
State 0, Symbol 2 -> Write 1, Move right, New State 3
State 0, Symbol 3 -> Write 3, Move left, New State 3
State 1, Symbol 0 -> Write 2, Move up, New State 2
State 1, Symbol 1 -> Write 1, Move down, New State 0
State 1, Symbol 2 -> Write 0, Move down, New State 1
State 1, Symbol 3 -> Write 0, Move left, New State 0
State 2, Symbol 0 -> Write 2, Move down, New State 2
State 2, Symbol 1 -> Write 2, Move down, New State 0
State 2, Symbol 2 -> Write 3, Move up, New State 1
State 2, Symbol 3 -> Write 2, Move left, New State 2
State 3, Symbol 0 -> Write 3, Move left, New State 1
State 3, Symbol 1 -> Write 0, Move left, New State 2
State 3, Symbol 2 -> Write 2, Move down, New State 3
State 3, Symbol 3 -> Write 3, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 1) with State 0 on Symbol 3 that is (3).
Question: where will the head be after 4 steps?
Options:
1: (1, 0)
2: (2, 1)
3: (2, 2)
4: (1, 1)
5: (0, 0)
6: (0, 2)
7: (1, 2)
8: (3, 2)
| 4 | [
"(1, 0)",
"(2, 1)",
"(2, 2)",
"(1, 1)",
"(0, 0)",
"(0, 2)",
"(1, 2)",
"(3, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 3
- **Symbol Written on (1, 1):** 3
- **New Position:** (1, 0)
- **New State:** 3
Step 2:
- **Position:** (1, 0)
- **State:** 3
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: <3>
- **Action:** Write 3, Move right, New State 0
- **Symbol Written on (1, 0):** 3
- **New Position:** (1, 1)
- **New State:** 0
Step 3:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 3
- **Symbol Written on (1, 1):** 3
- **New Position:** (1, 0)
- **New State:** 3
Step 4:
- **Position:** (1, 0)
- **State:** 3
- **Symbol:** According to step 2, it has been changed to symbol 3
- **State and Symbol**: <3>
- **Action:** Write 3, Move right, New State 0
- **Symbol Written on (1, 0):** 3
- **New Position:** (1, 1)
- **New State:** 0
Therefore, the final position after 4 steps will be (1, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00013 | games_images_test/2d_turing_machine/00013.png | states/00013.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move right, New State 1
State 0, Symbol 1 -> Write 4, Move right, New State 1
State 0, Symbol 2 -> Write 1, Move right, New State 0
State 0, Symbol 3 -> Write 3, Move right, New State 1
State 0, Symbol 4 -> Write 4, Move left, New State 1
State 1, Symbol 0 -> Write 2, Move up, New State 1
State 1, Symbol 1 -> Write 3, Move down, New State 2
State 1, Symbol 2 -> Write 1, Move left, New State 0
State 1, Symbol 3 -> Write 3, Move up, New State 1
State 1, Symbol 4 -> Write 4, Move down, New State 1
State 2, Symbol 0 -> Write 0, Move left, New State 0
State 2, Symbol 1 -> Write 4, Move right, New State 2
State 2, Symbol 2 -> Write 4, Move right, New State 2
State 2, Symbol 3 -> Write 3, Move down, New State 2
State 2, Symbol 4 -> Write 2, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 0) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 4 steps?
Options:
1: (0, 2)
2: (1, 0)
3: (2, 2)
4: (2, 1)
5: (0, 1)
6: (2, 0)
7: (3, 2)
8: (1, 2)
| 4 | [
"(0, 2)",
"(1, 0)",
"(2, 2)",
"(2, 1)",
"(0, 1)",
"(2, 0)",
"(3, 2)",
"(1, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 4, Move right, New State 1
- **Symbol Written on (1, 0):** 4
- **New Position:** (1, 1)
- **New State:** 1
Step 2:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: [4]
- **Action:** Write 4, Move down, New State 1
- **Symbol Written on (1, 1):** 4
- **New Position:** (2, 1)
- **New State:** 1
Step 3:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: [4]
- **Action:** Write 4, Move down, New State 1
- **Symbol Written on (2, 1):** 4
- **New Position:** (3, 1)
- **New State:** 1
Step 4:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (3, 1):** 3
- **New Position:** (2, 1)
- **New State:** 1
Therefore, the final position after 4 steps will be (2, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00014 | games_images_test/2d_turing_machine/00014.png | states/00014.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move left, New State 0
State 0, Symbol 1 -> Write 0, Move down, New State 1
State 0, Symbol 2 -> Write 3, Move left, New State 0
State 0, Symbol 3 -> Write 1, Move right, New State 1
State 1, Symbol 0 -> Write 1, Move left, New State 0
State 1, Symbol 1 -> Write 1, Move up, New State 1
State 1, Symbol 2 -> Write 1, Move right, New State 0
State 1, Symbol 3 -> Write 1, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 1) with State 1 on Symbol 1 that is [1].
Question: where will the head be after 8 steps?
Options:
1: (3, 3)
2: (2, 3)
3: (2, 2)
4: (0, 0)
5: (1, 1)
6: (4, 3)
7: (1, 0)
8: (0, 1)
| 5 | [
"(3, 3)",
"(2, 3)",
"(2, 2)",
"(0, 0)",
"(1, 1)",
"(4, 3)",
"(1, 0)",
"(0, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (3, 1):** 1
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (2, 1):** 1
- **New Position:** (1, 1)
- **New State:** 1
Step 3:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 1, Move right, New State 0
- **Symbol Written on (1, 1):** 1
- **New Position:** (1, 2)
- **New State:** 0
Step 4:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 0, Move down, New State 1
- **Symbol Written on (1, 2):** 0
- **New Position:** (2, 2)
- **New State:** 1
Step 5:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (2, 2):** 1
- **New Position:** (1, 2)
- **New State:** 1
Step 6:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** According to step 4, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 1, Move left, New State 0
- **Symbol Written on (1, 2):** 1
- **New Position:** (1, 1)
- **New State:** 0
Step 7:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 0, Move down, New State 1
- **Symbol Written on (1, 1):** 0
- **New Position:** (2, 1)
- **New State:** 1
Step 8:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** According to step 2, it has been changed to symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (2, 1):** 1
- **New Position:** (1, 1)
- **New State:** 1
Therefore, the final position after 8 steps will be (1, 1).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00015 | games_images_test/2d_turing_machine/00015.png | states/00015.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move left, New State 0
State 0, Symbol 1 -> Write 2, Move right, New State 0
State 0, Symbol 2 -> Write 2, Move down, New State 1
State 1, Symbol 0 -> Write 0, Move right, New State 0
State 1, Symbol 1 -> Write 0, Move left, New State 1
State 1, Symbol 2 -> Write 2, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (0, 1) with State 1 on Symbol 0 that is [0].
Question: where will the head be after 6 steps?
Options:
1: (3, 2)
2: (2, 1)
3: (1, 0)
4: (3, 0)
5: (1, 2)
6: (3, 1)
7: (0, 1)
8: (2, 2)
| 5 | [
"(3, 2)",
"(2, 1)",
"(1, 0)",
"(3, 0)",
"(1, 2)",
"(3, 1)",
"(0, 1)",
"(2, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (0, 1):** 0
- **New Position:** (0, 2)
- **New State:** 0
Step 2:
- **Position:** (0, 2)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (0, 2):** 2
- **New Position:** (1, 2)
- **New State:** 1
Step 3:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (1, 2):** 2
- **New Position:** (0, 2)
- **New State:** 0
Step 4:
- **Position:** (0, 2)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (0, 2):** 2
- **New Position:** (1, 2)
- **New State:** 1
Step 5:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (1, 2):** 2
- **New Position:** (0, 2)
- **New State:** 0
Step 6:
- **Position:** (0, 2)
- **State:** 0
- **Symbol:** According to step 4, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (0, 2):** 2
- **New Position:** (1, 2)
- **New State:** 1
Therefore, the final position after 6 steps will be (1, 2).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00016 | games_images_test/2d_turing_machine/00016.png | states/00016.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move up, New State 1
State 0, Symbol 1 -> Write 0, Move right, New State 1
State 0, Symbol 2 -> Write 0, Move up, New State 2
State 0, Symbol 3 -> Write 3, Move left, New State 1
State 1, Symbol 0 -> Write 0, Move right, New State 2
State 1, Symbol 1 -> Write 1, Move up, New State 1
State 1, Symbol 2 -> Write 2, Move right, New State 2
State 1, Symbol 3 -> Write 0, Move down, New State 0
State 2, Symbol 0 -> Write 3, Move down, New State 2
State 2, Symbol 1 -> Write 0, Move left, New State 3
State 2, Symbol 2 -> Write 3, Move down, New State 0
State 2, Symbol 3 -> Write 2, Move down, New State 0
State 3, Symbol 0 -> Write 3, Move up, New State 1
State 3, Symbol 1 -> Write 0, Move up, New State 1
State 3, Symbol 2 -> Write 3, Move up, New State 1
State 3, Symbol 3 -> Write 1, Move up, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 1) with State 3 on Symbol 0 that is <0>.
Question: where will the head be after 6 steps?
Options:
1: (4, 3)
2: (2, 0)
3: (3, 2)
4: (0, 1)
5: (2, 2)
6: (2, 1)
7: (1, 1)
8: (3, 3)
| 7 | [
"(4, 3)",
"(2, 0)",
"(3, 2)",
"(0, 1)",
"(2, 2)",
"(2, 1)",
"(1, 1)",
"(3, 3)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 3
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: <0>
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (3, 1):** 3
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (2, 1):** 1
- **New Position:** (1, 1)
- **New State:** 1
Step 3:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move right, New State 2
- **Symbol Written on (1, 1):** 2
- **New Position:** (1, 2)
- **New State:** 2
Step 4:
- **Position:** (1, 2)
- **State:** 2
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: {3}
- **Action:** Write 2, Move down, New State 0
- **Symbol Written on (1, 2):** 2
- **New Position:** (2, 2)
- **New State:** 0
Step 5:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (2, 2):** 3
- **New Position:** (2, 1)
- **New State:** 1
Step 6:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** According to step 2, it has been changed to symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (2, 1):** 1
- **New Position:** (1, 1)
- **New State:** 1
Therefore, the final position after 6 steps will be (1, 1).
The answer is option 7. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00017 | games_images_test/2d_turing_machine/00017.png | states/00017.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move down, New State 2
State 0, Symbol 1 -> Write 3, Move right, New State 2
State 0, Symbol 2 -> Write 1, Move up, New State 1
State 0, Symbol 3 -> Write 3, Move left, New State 0
State 1, Symbol 0 -> Write 3, Move down, New State 2
State 1, Symbol 1 -> Write 1, Move down, New State 1
State 1, Symbol 2 -> Write 1, Move down, New State 0
State 1, Symbol 3 -> Write 0, Move left, New State 0
State 2, Symbol 0 -> Write 0, Move right, New State 2
State 2, Symbol 1 -> Write 3, Move left, New State 1
State 2, Symbol 2 -> Write 1, Move up, New State 0
State 2, Symbol 3 -> Write 2, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 2) with State 1 on Symbol 0 that is [0].
Question: where will the head be after 4 steps?
Options:
1: (3, 1)
2: (3, 2)
3: (0, 0)
4: (1, 2)
5: (0, 1)
6: (3, 0)
7: (0, 2)
8: (1, 1)
| 3 | [
"(3, 1)",
"(3, 2)",
"(0, 0)",
"(1, 2)",
"(0, 1)",
"(3, 0)",
"(0, 2)",
"(1, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 3, Move down, New State 2
- **Symbol Written on (0, 2):** 3
- **New Position:** (1, 2)
- **New State:** 2
Step 2:
- **Position:** (1, 2)
- **State:** 2
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: {2}
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (1, 2):** 1
- **New Position:** (0, 2)
- **New State:** 0
Step 3:
- **Position:** (0, 2)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 0
- **Symbol Written on (0, 2):** 3
- **New Position:** (0, 1)
- **New State:** 0
Step 4:
- **Position:** (0, 1)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 0
- **Symbol Written on (0, 1):** 3
- **New Position:** (0, 0)
- **New State:** 0
Therefore, the final position after 4 steps will be (0, 0).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00018 | games_images_test/2d_turing_machine/00018.png | states/00018.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move up, New State 1
State 0, Symbol 1 -> Write 0, Move down, New State 0
State 0, Symbol 2 -> Write 0, Move left, New State 2
State 1, Symbol 0 -> Write 1, Move left, New State 2
State 1, Symbol 1 -> Write 0, Move down, New State 2
State 1, Symbol 2 -> Write 2, Move left, New State 2
State 2, Symbol 0 -> Write 1, Move right, New State 2
State 2, Symbol 1 -> Write 2, Move down, New State 0
State 2, Symbol 2 -> Write 0, Move down, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 0) with State 2 on Symbol 0 that is {0}.
Question: where will the head be after 5 steps?
Options:
1: (2, 2)
2: (0, 1)
3: (2, 1)
4: (1, 0)
5: (1, 2)
6: (1, 1)
7: (2, 0)
8: (0, 2)
| 6 | [
"(2, 2)",
"(0, 1)",
"(2, 1)",
"(1, 0)",
"(1, 2)",
"(1, 1)",
"(2, 0)",
"(0, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 1, Move right, New State 2
- **Symbol Written on (1, 0):** 1
- **New Position:** (1, 1)
- **New State:** 2
Step 2:
- **Position:** (1, 1)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 1, Move right, New State 2
- **Symbol Written on (1, 1):** 1
- **New Position:** (1, 2)
- **New State:** 2
Step 3:
- **Position:** (1, 2)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 2, Move down, New State 0
- **Symbol Written on (1, 2):** 2
- **New Position:** (2, 2)
- **New State:** 0
Step 4:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move up, New State 1
- **Symbol Written on (2, 2):** 2
- **New Position:** (1, 2)
- **New State:** 1
Step 5:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move left, New State 2
- **Symbol Written on (1, 2):** 2
- **New Position:** (1, 1)
- **New State:** 2
Therefore, the final position after 5 steps will be (1, 1).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00019 | games_images_test/2d_turing_machine/00019.png | states/00019.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move down, New State 0
State 0, Symbol 1 -> Write 0, Move up, New State 0
State 0, Symbol 2 -> Write 1, Move up, New State 1
State 1, Symbol 0 -> Write 1, Move down, New State 0
State 1, Symbol 1 -> Write 0, Move down, New State 1
State 1, Symbol 2 -> Write 1, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 3) with State 1 on Symbol 2 that is [2].
Question: where will the head be after 6 steps?
Options:
1: (1, 3)
2: (4, 0)
3: (3, 0)
4: (4, 3)
5: (3, 3)
6: (1, 2)
7: (1, 0)
8: (2, 3)
| 5 | [
"(1, 3)",
"(4, 0)",
"(3, 0)",
"(4, 3)",
"(3, 3)",
"(1, 2)",
"(1, 0)",
"(2, 3)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 3)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (3, 3):** 1
- **New Position:** (2, 3)
- **New State:** 0
Step 2:
- **Position:** (2, 3)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (2, 3):** 0
- **New Position:** (1, 3)
- **New State:** 0
Step 3:
- **Position:** (1, 3)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (1, 3):** 0
- **New Position:** (2, 3)
- **New State:** 0
Step 4:
- **Position:** (2, 3)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (2, 3):** 0
- **New Position:** (3, 3)
- **New State:** 0
Step 5:
- **Position:** (3, 3)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (3, 3):** 0
- **New Position:** (2, 3)
- **New State:** 0
Step 6:
- **Position:** (2, 3)
- **State:** 0
- **Symbol:** According to step 4, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (2, 3):** 0
- **New Position:** (3, 3)
- **New State:** 0
Therefore, the final position after 6 steps will be (3, 3).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00020 | games_images_test/2d_turing_machine/00020.png | states/00020.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move down, New State 0
State 0, Symbol 1 -> Write 1, Move down, New State 1
State 0, Symbol 2 -> Write 0, Move right, New State 1
State 1, Symbol 0 -> Write 1, Move left, New State 0
State 1, Symbol 1 -> Write 2, Move up, New State 0
State 1, Symbol 2 -> Write 2, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (1, 2) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 5 steps?
Options:
1: (0, 2)
2: (2, 2)
3: (0, 1)
4: (3, 2)
5: (1, 1)
6: (4, 2)
7: (2, 1)
8: (4, 0)
| 2 | [
"(0, 2)",
"(2, 2)",
"(0, 1)",
"(3, 2)",
"(1, 1)",
"(4, 2)",
"(2, 1)",
"(4, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 1
- **Symbol Written on (1, 2):** 1
- **New Position:** (2, 2)
- **New State:** 1
Step 2:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (2, 2):** 2
- **New Position:** (1, 2)
- **New State:** 0
Step 3:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 1
- **Symbol Written on (1, 2):** 1
- **New Position:** (2, 2)
- **New State:** 1
Step 4:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** According to step 2, it has been changed to symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (2, 2):** 2
- **New Position:** (1, 2)
- **New State:** 0
Step 5:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 1
- **Symbol Written on (1, 2):** 1
- **New Position:** (2, 2)
- **New State:** 1
Therefore, the final position after 5 steps will be (2, 2).
The answer is option 2. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00021 | games_images_test/2d_turing_machine/00021.png | states/00021.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move right, New State 2
State 0, Symbol 1 -> Write 2, Move up, New State 2
State 0, Symbol 2 -> Write 3, Move left, New State 2
State 0, Symbol 3 -> Write 3, Move down, New State 2
State 1, Symbol 0 -> Write 2, Move down, New State 0
State 1, Symbol 1 -> Write 0, Move up, New State 1
State 1, Symbol 2 -> Write 3, Move up, New State 2
State 1, Symbol 3 -> Write 2, Move left, New State 0
State 2, Symbol 0 -> Write 2, Move right, New State 2
State 2, Symbol 1 -> Write 0, Move down, New State 1
State 2, Symbol 2 -> Write 1, Move up, New State 1
State 2, Symbol 3 -> Write 1, Move down, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 4) with State 0 on Symbol 2 that is (2).
Question: where will the head be after 4 steps?
Options:
1: (2, 3)
2: (2, 0)
3: (4, 3)
4: (1, 1)
5: (1, 3)
6: (4, 2)
7: (3, 0)
8: (2, 4)
| 8 | [
"(2, 3)",
"(2, 0)",
"(4, 3)",
"(1, 1)",
"(1, 3)",
"(4, 2)",
"(3, 0)",
"(2, 4)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 4)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 3, Move left, New State 2
- **Symbol Written on (2, 4):** 3
- **New Position:** (2, 3)
- **New State:** 2
Step 2:
- **Position:** (2, 3)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 2, Move right, New State 2
- **Symbol Written on (2, 3):** 2
- **New Position:** (2, 4)
- **New State:** 2
Step 3:
- **Position:** (2, 4)
- **State:** 2
- **Symbol:** According to step 1, it has been changed to symbol 3
- **State and Symbol**: {3}
- **Action:** Write 1, Move down, New State 2
- **Symbol Written on (2, 4):** 1
- **New Position:** (3, 4)
- **New State:** 2
Step 4:
- **Position:** (3, 4)
- **State:** 2
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: {2}
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (3, 4):** 1
- **New Position:** (2, 4)
- **New State:** 1
Therefore, the final position after 4 steps will be (2, 4).
The answer is option 8. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00022 | games_images_test/2d_turing_machine/00022.png | states/00022.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move up, New State 1
State 0, Symbol 1 -> Write 0, Move right, New State 1
State 0, Symbol 2 -> Write 0, Move left, New State 1
State 0, Symbol 3 -> Write 0, Move up, New State 2
State 0, Symbol 4 -> Write 2, Move left, New State 0
State 1, Symbol 0 -> Write 4, Move up, New State 1
State 1, Symbol 1 -> Write 3, Move up, New State 0
State 1, Symbol 2 -> Write 4, Move down, New State 2
State 1, Symbol 3 -> Write 4, Move right, New State 0
State 1, Symbol 4 -> Write 4, Move up, New State 1
State 2, Symbol 0 -> Write 4, Move down, New State 1
State 2, Symbol 1 -> Write 0, Move down, New State 2
State 2, Symbol 2 -> Write 0, Move left, New State 2
State 2, Symbol 3 -> Write 2, Move right, New State 0
State 2, Symbol 4 -> Write 3, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 0) with State 2 on Symbol 0 that is {0}.
Question: where will the head be after 7 steps?
Options:
1: (3, 0)
2: (0, 4)
3: (4, 2)
4: (4, 0)
5: (3, 2)
6: (3, 3)
7: (0, 3)
8: (2, 2)
| 8 | [
"(3, 0)",
"(0, 4)",
"(4, 2)",
"(4, 0)",
"(3, 2)",
"(3, 3)",
"(0, 3)",
"(2, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 0)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 4, Move down, New State 1
- **Symbol Written on (3, 0):** 4
- **New Position:** (4, 0)
- **New State:** 1
Step 2:
- **Position:** (4, 0)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 4, Move right, New State 0
- **Symbol Written on (4, 0):** 4
- **New Position:** (4, 1)
- **New State:** 0
Step 3:
- **Position:** (4, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 0, Move right, New State 1
- **Symbol Written on (4, 1):** 0
- **New Position:** (4, 2)
- **New State:** 1
Step 4:
- **Position:** (4, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 4, Move up, New State 1
- **Symbol Written on (4, 2):** 4
- **New Position:** (3, 2)
- **New State:** 1
Step 5:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 4, Move up, New State 1
- **Symbol Written on (3, 2):** 4
- **New Position:** (2, 2)
- **New State:** 1
Step 6:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 4, Move down, New State 2
- **Symbol Written on (2, 2):** 4
- **New Position:** (3, 2)
- **New State:** 2
Step 7:
- **Position:** (3, 2)
- **State:** 2
- **Symbol:** According to step 5, it has been changed to symbol 4
- **State and Symbol**: {4}
- **Action:** Write 3, Move up, New State 0
- **Symbol Written on (3, 2):** 3
- **New Position:** (2, 2)
- **New State:** 0
Therefore, the final position after 7 steps will be (2, 2).
The answer is option 8. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00023 | games_images_test/2d_turing_machine/00023.png | states/00023.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move down, New State 2
State 0, Symbol 1 -> Write 2, Move up, New State 0
State 0, Symbol 2 -> Write 0, Move right, New State 1
State 0, Symbol 3 -> Write 4, Move up, New State 1
State 0, Symbol 4 -> Write 3, Move right, New State 1
State 1, Symbol 0 -> Write 1, Move down, New State 2
State 1, Symbol 1 -> Write 3, Move up, New State 1
State 1, Symbol 2 -> Write 0, Move right, New State 0
State 1, Symbol 3 -> Write 0, Move up, New State 2
State 1, Symbol 4 -> Write 2, Move left, New State 1
State 2, Symbol 0 -> Write 3, Move down, New State 0
State 2, Symbol 1 -> Write 0, Move right, New State 1
State 2, Symbol 2 -> Write 0, Move down, New State 0
State 2, Symbol 3 -> Write 2, Move up, New State 2
State 2, Symbol 4 -> Write 1, Move up, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 0) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 7 steps?
Options:
1: (3, 1)
2: (3, 0)
3: (2, 0)
4: (0, 0)
5: (2, 2)
6: (3, 2)
7: (1, 0)
8: (0, 1)
| 4 | [
"(3, 1)",
"(3, 0)",
"(2, 0)",
"(0, 0)",
"(2, 2)",
"(3, 2)",
"(1, 0)",
"(0, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (1, 0):** 2
- **New Position:** (0, 0)
- **New State:** 0
Step 2:
- **Position:** (0, 0)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move down, New State 2
- **Symbol Written on (0, 0):** 0
- **New Position:** (1, 0)
- **New State:** 2
Step 3:
- **Position:** (1, 0)
- **State:** 2
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: {2}
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (1, 0):** 0
- **New Position:** (2, 0)
- **New State:** 0
Step 4:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 4, Move up, New State 1
- **Symbol Written on (2, 0):** 4
- **New Position:** (1, 0)
- **New State:** 1
Step 5:
- **Position:** (1, 0)
- **State:** 1
- **Symbol:** According to step 3, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 1, Move down, New State 2
- **Symbol Written on (1, 0):** 1
- **New Position:** (2, 0)
- **New State:** 2
Step 6:
- **Position:** (2, 0)
- **State:** 2
- **Symbol:** According to step 4, it has been changed to symbol 4
- **State and Symbol**: {4}
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (2, 0):** 1
- **New Position:** (1, 0)
- **New State:** 1
Step 7:
- **Position:** (1, 0)
- **State:** 1
- **Symbol:** According to step 5, it has been changed to symbol 1
- **State and Symbol**: [1]
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (1, 0):** 3
- **New Position:** (0, 0)
- **New State:** 1
Therefore, the final position after 7 steps will be (0, 0).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00024 | games_images_test/2d_turing_machine/00024.png | states/00024.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move left, New State 0
State 0, Symbol 1 -> Write 2, Move down, New State 0
State 0, Symbol 2 -> Write 2, Move up, New State 2
State 1, Symbol 0 -> Write 1, Move up, New State 0
State 1, Symbol 1 -> Write 2, Move right, New State 1
State 1, Symbol 2 -> Write 2, Move right, New State 2
State 2, Symbol 0 -> Write 0, Move up, New State 2
State 2, Symbol 1 -> Write 2, Move down, New State 1
State 2, Symbol 2 -> Write 0, Move down, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (4, 3) with State 2 on Symbol 0 that is {0}.
Question: where will the head be after 7 steps?
Options:
1: (2, 0)
2: (3, 0)
3: (3, 2)
4: (1, 2)
5: (3, 1)
6: (0, 1)
7: (4, 3)
8: (0, 0)
| 5 | [
"(2, 0)",
"(3, 0)",
"(3, 2)",
"(1, 2)",
"(3, 1)",
"(0, 1)",
"(4, 3)",
"(0, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (4, 3)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 0, Move up, New State 2
- **Symbol Written on (4, 3):** 0
- **New Position:** (3, 3)
- **New State:** 2
Step 2:
- **Position:** (3, 3)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 0, Move up, New State 2
- **Symbol Written on (3, 3):** 0
- **New Position:** (2, 3)
- **New State:** 2
Step 3:
- **Position:** (2, 3)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 0, Move up, New State 2
- **Symbol Written on (2, 3):** 0
- **New Position:** (1, 3)
- **New State:** 2
Step 4:
- **Position:** (1, 3)
- **State:** 2
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: {2}
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (1, 3):** 0
- **New Position:** (2, 3)
- **New State:** 0
Step 5:
- **Position:** (2, 3)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move left, New State 0
- **Symbol Written on (2, 3):** 1
- **New Position:** (2, 2)
- **New State:** 0
Step 6:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move down, New State 0
- **Symbol Written on (2, 2):** 2
- **New Position:** (3, 2)
- **New State:** 0
Step 7:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move left, New State 0
- **Symbol Written on (3, 2):** 1
- **New Position:** (3, 1)
- **New State:** 0
Therefore, the final position after 7 steps will be (3, 1).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00025 | games_images_test/2d_turing_machine/00025.png | states/00025.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move down, New State 1
State 0, Symbol 1 -> Write 1, Move up, New State 2
State 0, Symbol 2 -> Write 1, Move left, New State 3
State 1, Symbol 0 -> Write 2, Move down, New State 1
State 1, Symbol 1 -> Write 1, Move left, New State 2
State 1, Symbol 2 -> Write 2, Move up, New State 2
State 2, Symbol 0 -> Write 1, Move up, New State 1
State 2, Symbol 1 -> Write 2, Move left, New State 3
State 2, Symbol 2 -> Write 0, Move right, New State 3
State 3, Symbol 0 -> Write 0, Move left, New State 2
State 3, Symbol 1 -> Write 1, Move left, New State 0
State 3, Symbol 2 -> Write 1, Move down, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 1) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 3 steps?
Options:
1: (2, 0)
2: (3, 0)
3: (1, 0)
4: (3, 1)
5: (0, 0)
6: (1, 2)
7: (3, 2)
8: (1, 1)
| 4 | [
"(2, 0)",
"(3, 0)",
"(1, 0)",
"(3, 1)",
"(0, 0)",
"(1, 2)",
"(3, 2)",
"(1, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move down, New State 1
- **Symbol Written on (0, 1):** 1
- **New Position:** (1, 1)
- **New State:** 1
Step 2:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (1, 1):** 2
- **New Position:** (2, 1)
- **New State:** 1
Step 3:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (2, 1):** 2
- **New Position:** (3, 1)
- **New State:** 1
Therefore, the final position after 3 steps will be (3, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00026 | games_images_test/2d_turing_machine/00026.png | states/00026.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move up, New State 0
State 0, Symbol 1 -> Write 1, Move left, New State 2
State 0, Symbol 2 -> Write 0, Move up, New State 1
State 0, Symbol 3 -> Write 0, Move left, New State 2
State 0, Symbol 4 -> Write 3, Move up, New State 0
State 1, Symbol 0 -> Write 3, Move right, New State 1
State 1, Symbol 1 -> Write 0, Move left, New State 2
State 1, Symbol 2 -> Write 4, Move left, New State 1
State 1, Symbol 3 -> Write 3, Move right, New State 0
State 1, Symbol 4 -> Write 4, Move right, New State 0
State 2, Symbol 0 -> Write 0, Move left, New State 1
State 2, Symbol 1 -> Write 4, Move left, New State 3
State 2, Symbol 2 -> Write 1, Move down, New State 2
State 2, Symbol 3 -> Write 0, Move down, New State 1
State 2, Symbol 4 -> Write 4, Move left, New State 1
State 3, Symbol 0 -> Write 4, Move down, New State 1
State 3, Symbol 1 -> Write 1, Move left, New State 0
State 3, Symbol 2 -> Write 3, Move left, New State 3
State 3, Symbol 3 -> Write 4, Move down, New State 0
State 3, Symbol 4 -> Write 1, Move right, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 0) with State 3 on Symbol 0 that is <0>.
Question: where will the head be after 7 steps?
Options:
1: (3, 2)
2: (0, 1)
3: (2, 1)
4: (0, 0)
5: (0, 2)
6: (2, 2)
7: (2, 0)
8: (3, 1)
| 3 | [
"(3, 2)",
"(0, 1)",
"(2, 1)",
"(0, 0)",
"(0, 2)",
"(2, 2)",
"(2, 0)",
"(3, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 0)
- **State:** 3
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: <0>
- **Action:** Write 4, Move down, New State 1
- **Symbol Written on (0, 0):** 4
- **New Position:** (1, 0)
- **New State:** 1
Step 2:
- **Position:** (1, 0)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 3, Move right, New State 1
- **Symbol Written on (1, 0):** 3
- **New Position:** (1, 1)
- **New State:** 1
Step 3:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 3, Move right, New State 0
- **Symbol Written on (1, 1):** 3
- **New Position:** (1, 2)
- **New State:** 0
Step 4:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move left, New State 2
- **Symbol Written on (1, 2):** 1
- **New Position:** (1, 1)
- **New State:** 2
Step 5:
- **Position:** (1, 1)
- **State:** 2
- **Symbol:** According to step 3, it has been changed to symbol 3
- **State and Symbol**: {3}
- **Action:** Write 0, Move down, New State 1
- **Symbol Written on (1, 1):** 0
- **New Position:** (2, 1)
- **New State:** 1
Step 6:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: [4]
- **Action:** Write 4, Move right, New State 0
- **Symbol Written on (2, 1):** 4
- **New Position:** (2, 2)
- **New State:** 0
Step 7:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 0, Move left, New State 2
- **Symbol Written on (2, 2):** 0
- **New Position:** (2, 1)
- **New State:** 2
Therefore, the final position after 7 steps will be (2, 1).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00027 | games_images_test/2d_turing_machine/00027.png | states/00027.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move down, New State 3
State 0, Symbol 1 -> Write 1, Move left, New State 3
State 0, Symbol 2 -> Write 3, Move up, New State 0
State 0, Symbol 3 -> Write 0, Move down, New State 1
State 1, Symbol 0 -> Write 1, Move up, New State 0
State 1, Symbol 1 -> Write 3, Move up, New State 2
State 1, Symbol 2 -> Write 3, Move up, New State 3
State 1, Symbol 3 -> Write 0, Move right, New State 3
State 2, Symbol 0 -> Write 0, Move up, New State 3
State 2, Symbol 1 -> Write 0, Move right, New State 3
State 2, Symbol 2 -> Write 2, Move up, New State 3
State 2, Symbol 3 -> Write 1, Move right, New State 0
State 3, Symbol 0 -> Write 0, Move left, New State 3
State 3, Symbol 1 -> Write 3, Move down, New State 1
State 3, Symbol 2 -> Write 0, Move down, New State 0
State 3, Symbol 3 -> Write 0, Move down, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 2) with State 1 on Symbol 0 that is [0].
Question: where will the head be after 6 steps?
Options:
1: (1, 2)
2: (0, 2)
3: (2, 3)
4: (4, 3)
5: (1, 3)
6: (3, 2)
7: (2, 2)
8: (2, 0)
| 8 | [
"(1, 2)",
"(0, 2)",
"(2, 3)",
"(4, 3)",
"(1, 3)",
"(3, 2)",
"(2, 2)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (2, 2):** 1
- **New Position:** (1, 2)
- **New State:** 0
Step 2:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move left, New State 3
- **Symbol Written on (1, 2):** 1
- **New Position:** (1, 1)
- **New State:** 3
Step 3:
- **Position:** (1, 1)
- **State:** 3
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: <0>
- **Action:** Write 0, Move left, New State 3
- **Symbol Written on (1, 1):** 0
- **New Position:** (1, 0)
- **New State:** 3
Step 4:
- **Position:** (1, 0)
- **State:** 3
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: <1>
- **Action:** Write 3, Move down, New State 1
- **Symbol Written on (1, 0):** 3
- **New Position:** (2, 0)
- **New State:** 1
Step 5:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 3, Move up, New State 3
- **Symbol Written on (2, 0):** 3
- **New Position:** (1, 0)
- **New State:** 3
Step 6:
- **Position:** (1, 0)
- **State:** 3
- **Symbol:** According to step 4, it has been changed to symbol 3
- **State and Symbol**: <3>
- **Action:** Write 0, Move down, New State 2
- **Symbol Written on (1, 0):** 0
- **New Position:** (2, 0)
- **New State:** 2
Therefore, the final position after 6 steps will be (2, 0).
The answer is option 8. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00028 | games_images_test/2d_turing_machine/00028.png | states/00028.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move right, New State 1
State 0, Symbol 1 -> Write 2, Move left, New State 0
State 0, Symbol 2 -> Write 0, Move down, New State 1
State 1, Symbol 0 -> Write 1, Move up, New State 0
State 1, Symbol 1 -> Write 1, Move up, New State 0
State 1, Symbol 2 -> Write 0, Move down, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 0) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 3 steps?
Options:
1: (1, 1)
2: (0, 1)
3: (0, 0)
4: (1, 0)
5: (3, 1)
6: (2, 1)
7: (1, 2)
8: (2, 0)
| 5 | [
"(1, 1)",
"(0, 1)",
"(0, 0)",
"(1, 0)",
"(3, 1)",
"(2, 1)",
"(1, 2)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move right, New State 1
- **Symbol Written on (3, 0):** 1
- **New Position:** (3, 1)
- **New State:** 1
Step 2:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (3, 1):** 1
- **New Position:** (2, 1)
- **New State:** 0
Step 3:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move down, New State 1
- **Symbol Written on (2, 1):** 0
- **New Position:** (3, 1)
- **New State:** 1
Therefore, the final position after 3 steps will be (3, 1).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00029 | games_images_test/2d_turing_machine/00029.png | states/00029.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move right, New State 2
State 0, Symbol 1 -> Write 0, Move up, New State 0
State 0, Symbol 2 -> Write 0, Move right, New State 2
State 1, Symbol 0 -> Write 2, Move right, New State 2
State 1, Symbol 1 -> Write 2, Move up, New State 2
State 1, Symbol 2 -> Write 0, Move left, New State 2
State 2, Symbol 0 -> Write 2, Move left, New State 2
State 2, Symbol 1 -> Write 1, Move up, New State 0
State 2, Symbol 2 -> Write 2, Move down, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 1) with State 2 on Symbol 1 that is {1}.
Question: where will the head be after 6 steps?
Options:
1: (2, 1)
2: (4, 3)
3: (3, 3)
4: (1, 0)
5: (1, 1)
6: (2, 2)
7: (1, 3)
8: (0, 4)
| 7 | [
"(2, 1)",
"(4, 3)",
"(3, 3)",
"(1, 0)",
"(1, 1)",
"(2, 2)",
"(1, 3)",
"(0, 4)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (3, 1):** 1
- **New Position:** (2, 1)
- **New State:** 0
Step 2:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move right, New State 2
- **Symbol Written on (2, 1):** 0
- **New Position:** (2, 2)
- **New State:** 2
Step 3:
- **Position:** (2, 2)
- **State:** 2
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: {2}
- **Action:** Write 2, Move down, New State 0
- **Symbol Written on (2, 2):** 2
- **New Position:** (3, 2)
- **New State:** 0
Step 4:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (3, 2):** 0
- **New Position:** (2, 2)
- **New State:** 0
Step 5:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move right, New State 2
- **Symbol Written on (2, 2):** 0
- **New Position:** (2, 3)
- **New State:** 2
Step 6:
- **Position:** (2, 3)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (2, 3):** 1
- **New Position:** (1, 3)
- **New State:** 0
Therefore, the final position after 6 steps will be (1, 3).
The answer is option 7. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00030 | games_images_test/2d_turing_machine/00030.png | states/00030.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 3, Move left, New State 1
State 0, Symbol 1 -> Write 3, Move up, New State 1
State 0, Symbol 2 -> Write 3, Move up, New State 1
State 0, Symbol 3 -> Write 2, Move right, New State 3
State 1, Symbol 0 -> Write 2, Move left, New State 3
State 1, Symbol 1 -> Write 2, Move down, New State 3
State 1, Symbol 2 -> Write 2, Move down, New State 3
State 1, Symbol 3 -> Write 2, Move down, New State 3
State 2, Symbol 0 -> Write 0, Move right, New State 3
State 2, Symbol 1 -> Write 2, Move left, New State 2
State 2, Symbol 2 -> Write 1, Move down, New State 3
State 2, Symbol 3 -> Write 0, Move down, New State 2
State 3, Symbol 0 -> Write 1, Move left, New State 3
State 3, Symbol 1 -> Write 3, Move down, New State 0
State 3, Symbol 2 -> Write 1, Move down, New State 3
State 3, Symbol 3 -> Write 3, Move left, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 2) with State 0 on Symbol 2 that is (2).
Question: where will the head be after 5 steps?
Options:
1: (1, 0)
2: (2, 1)
3: (2, 2)
4: (1, 1)
5: (3, 2)
6: (3, 1)
7: (0, 0)
8: (0, 2)
| 4 | [
"(1, 0)",
"(2, 1)",
"(2, 2)",
"(1, 1)",
"(3, 2)",
"(3, 1)",
"(0, 0)",
"(0, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (1, 2):** 3
- **New Position:** (0, 2)
- **New State:** 1
Step 2:
- **Position:** (0, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 2, Move down, New State 3
- **Symbol Written on (0, 2):** 2
- **New Position:** (1, 2)
- **New State:** 3
Step 3:
- **Position:** (1, 2)
- **State:** 3
- **Symbol:** According to step 1, it has been changed to symbol 3
- **State and Symbol**: <3>
- **Action:** Write 3, Move left, New State 0
- **Symbol Written on (1, 2):** 3
- **New Position:** (1, 1)
- **New State:** 0
Step 4:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (1, 1):** 3
- **New Position:** (0, 1)
- **New State:** 1
Step 5:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move down, New State 3
- **Symbol Written on (0, 1):** 2
- **New Position:** (1, 1)
- **New State:** 3
Therefore, the final position after 5 steps will be (1, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00031 | games_images_test/2d_turing_machine/00031.png | states/00031.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move left, New State 1
State 0, Symbol 1 -> Write 2, Move left, New State 2
State 0, Symbol 2 -> Write 1, Move down, New State 2
State 0, Symbol 3 -> Write 1, Move left, New State 1
State 1, Symbol 0 -> Write 0, Move down, New State 2
State 1, Symbol 1 -> Write 1, Move up, New State 0
State 1, Symbol 2 -> Write 3, Move left, New State 3
State 1, Symbol 3 -> Write 1, Move right, New State 1
State 2, Symbol 0 -> Write 3, Move up, New State 0
State 2, Symbol 1 -> Write 1, Move right, New State 3
State 2, Symbol 2 -> Write 0, Move left, New State 0
State 2, Symbol 3 -> Write 3, Move up, New State 1
State 3, Symbol 0 -> Write 1, Move up, New State 1
State 3, Symbol 1 -> Write 2, Move up, New State 0
State 3, Symbol 2 -> Write 2, Move down, New State 2
State 3, Symbol 3 -> Write 1, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 2) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 6 steps?
Options:
1: (0, 1)
2: (2, 2)
3: (2, 0)
4: (3, 1)
5: (1, 1)
6: (0, 2)
7: (3, 0)
8: (3, 2)
| 4 | [
"(0, 1)",
"(2, 2)",
"(2, 0)",
"(3, 1)",
"(1, 1)",
"(0, 2)",
"(3, 0)",
"(3, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move left, New State 1
- **Symbol Written on (2, 2):** 2
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move down, New State 2
- **Symbol Written on (2, 1):** 0
- **New Position:** (3, 1)
- **New State:** 2
Step 3:
- **Position:** (3, 1)
- **State:** 2
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: {3}
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (3, 1):** 3
- **New Position:** (2, 1)
- **New State:** 1
Step 4:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** According to step 2, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move down, New State 2
- **Symbol Written on (2, 1):** 0
- **New Position:** (3, 1)
- **New State:** 2
Step 5:
- **Position:** (3, 1)
- **State:** 2
- **Symbol:** According to step 3, it has been changed to symbol 3
- **State and Symbol**: {3}
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (3, 1):** 3
- **New Position:** (2, 1)
- **New State:** 1
Step 6:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** According to step 4, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move down, New State 2
- **Symbol Written on (2, 1):** 0
- **New Position:** (3, 1)
- **New State:** 2
Therefore, the final position after 6 steps will be (3, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00032 | games_images_test/2d_turing_machine/00032.png | states/00032.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move down, New State 0
State 0, Symbol 1 -> Write 2, Move right, New State 1
State 0, Symbol 2 -> Write 0, Move up, New State 0
State 0, Symbol 3 -> Write 4, Move right, New State 1
State 0, Symbol 4 -> Write 3, Move down, New State 1
State 1, Symbol 0 -> Write 1, Move up, New State 1
State 1, Symbol 1 -> Write 1, Move down, New State 0
State 1, Symbol 2 -> Write 0, Move left, New State 1
State 1, Symbol 3 -> Write 2, Move up, New State 0
State 1, Symbol 4 -> Write 2, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (1, 1) with State 1 on Symbol 3 that is [3].
Question: where will the head be after 5 steps?
Options:
1: (2, 1)
2: (0, 1)
3: (4, 0)
4: (1, 1)
5: (0, 2)
6: (4, 2)
7: (1, 2)
8: (3, 2)
| 8 | [
"(2, 1)",
"(0, 1)",
"(4, 0)",
"(1, 1)",
"(0, 2)",
"(4, 2)",
"(1, 2)",
"(3, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (1, 1):** 2
- **New Position:** (0, 1)
- **New State:** 0
Step 2:
- **Position:** (0, 1)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 4, Move right, New State 1
- **Symbol Written on (0, 1):** 4
- **New Position:** (0, 2)
- **New State:** 1
Step 3:
- **Position:** (0, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (0, 2):** 1
- **New Position:** (1, 2)
- **New State:** 0
Step 4:
- **Position:** (1, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move down, New State 0
- **Symbol Written on (1, 2):** 2
- **New Position:** (2, 2)
- **New State:** 0
Step 5:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: (4)
- **Action:** Write 3, Move down, New State 1
- **Symbol Written on (2, 2):** 3
- **New Position:** (3, 2)
- **New State:** 1
Therefore, the final position after 5 steps will be (3, 2).
The answer is option 8. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00033 | games_images_test/2d_turing_machine/00033.png | states/00033.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move down, New State 1
State 0, Symbol 1 -> Write 0, Move left, New State 1
State 0, Symbol 2 -> Write 0, Move down, New State 0
State 1, Symbol 0 -> Write 0, Move up, New State 0
State 1, Symbol 1 -> Write 0, Move down, New State 1
State 1, Symbol 2 -> Write 0, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (1, 0) with State 1 on Symbol 0 that is [0].
Question: where will the head be after 4 steps?
Options:
1: (3, 2)
2: (0, 2)
3: (3, 0)
4: (0, 1)
5: (1, 0)
6: (4, 1)
7: (4, 0)
8: (0, 0)
| 3 | [
"(3, 2)",
"(0, 2)",
"(3, 0)",
"(0, 1)",
"(1, 0)",
"(4, 1)",
"(4, 0)",
"(0, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (1, 0):** 0
- **New Position:** (0, 0)
- **New State:** 0
Step 2:
- **Position:** (0, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (0, 0):** 0
- **New Position:** (1, 0)
- **New State:** 0
Step 3:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (1, 0):** 2
- **New Position:** (2, 0)
- **New State:** 1
Step 4:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 0, Move down, New State 1
- **Symbol Written on (2, 0):** 0
- **New Position:** (3, 0)
- **New State:** 1
Therefore, the final position after 4 steps will be (3, 0).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00034 | games_images_test/2d_turing_machine/00034.png | states/00034.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move left, New State 2
State 0, Symbol 1 -> Write 2, Move right, New State 0
State 0, Symbol 2 -> Write 0, Move left, New State 1
State 0, Symbol 3 -> Write 1, Move right, New State 2
State 1, Symbol 0 -> Write 0, Move down, New State 3
State 1, Symbol 1 -> Write 1, Move right, New State 0
State 1, Symbol 2 -> Write 3, Move down, New State 2
State 1, Symbol 3 -> Write 1, Move left, New State 1
State 2, Symbol 0 -> Write 1, Move right, New State 0
State 2, Symbol 1 -> Write 0, Move right, New State 0
State 2, Symbol 2 -> Write 0, Move left, New State 2
State 2, Symbol 3 -> Write 1, Move right, New State 3
State 3, Symbol 0 -> Write 0, Move down, New State 3
State 3, Symbol 1 -> Write 0, Move left, New State 1
State 3, Symbol 2 -> Write 2, Move up, New State 0
State 3, Symbol 3 -> Write 2, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 2) with State 0 on Symbol 2 that is (2).
Question: where will the head be after 5 steps?
Options:
1: (4, 2)
2: (4, 0)
3: (2, 1)
4: (0, 1)
5: (1, 0)
6: (1, 1)
7: (3, 2)
8: (2, 0)
| 4 | [
"(4, 2)",
"(4, 0)",
"(2, 1)",
"(0, 1)",
"(1, 0)",
"(1, 1)",
"(3, 2)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 2)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move left, New State 1
- **Symbol Written on (0, 2):** 0
- **New Position:** (0, 1)
- **New State:** 1
Step 2:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (0, 1):** 1
- **New Position:** (0, 0)
- **New State:** 1
Step 3:
- **Position:** (0, 0)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move right, New State 0
- **Symbol Written on (0, 0):** 1
- **New Position:** (0, 1)
- **New State:** 0
Step 4:
- **Position:** (0, 1)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move right, New State 0
- **Symbol Written on (0, 1):** 2
- **New Position:** (0, 2)
- **New State:** 0
Step 5:
- **Position:** (0, 2)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move left, New State 2
- **Symbol Written on (0, 2):** 2
- **New Position:** (0, 1)
- **New State:** 2
Therefore, the final position after 5 steps will be (0, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00035 | games_images_test/2d_turing_machine/00035.png | states/00035.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move left, New State 1
State 0, Symbol 1 -> Write 1, Move left, New State 1
State 0, Symbol 2 -> Write 0, Move up, New State 1
State 1, Symbol 0 -> Write 0, Move right, New State 0
State 1, Symbol 1 -> Write 2, Move left, New State 1
State 1, Symbol 2 -> Write 1, Move down, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (2, 2) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 5 steps?
Options:
1: (0, 0)
2: (2, 0)
3: (1, 0)
4: (1, 2)
5: (2, 2)
6: (2, 1)
7: (0, 2)
8: (1, 1)
| 6 | [
"(0, 0)",
"(2, 0)",
"(1, 0)",
"(1, 2)",
"(2, 2)",
"(2, 1)",
"(0, 2)",
"(1, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (2, 2):** 1
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (2, 1):** 0
- **New Position:** (2, 2)
- **New State:** 0
Step 3:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (2, 2):** 1
- **New Position:** (2, 1)
- **New State:** 1
Step 4:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** According to step 2, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (2, 1):** 0
- **New Position:** (2, 2)
- **New State:** 0
Step 5:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (2, 2):** 1
- **New Position:** (2, 1)
- **New State:** 1
Therefore, the final position after 5 steps will be (2, 1).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00036 | games_images_test/2d_turing_machine/00036.png | states/00036.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move up, New State 3
State 0, Symbol 1 -> Write 1, Move left, New State 3
State 0, Symbol 2 -> Write 2, Move left, New State 3
State 0, Symbol 3 -> Write 3, Move left, New State 0
State 1, Symbol 0 -> Write 3, Move left, New State 1
State 1, Symbol 1 -> Write 1, Move up, New State 2
State 1, Symbol 2 -> Write 2, Move right, New State 0
State 1, Symbol 3 -> Write 0, Move right, New State 2
State 2, Symbol 0 -> Write 2, Move right, New State 1
State 2, Symbol 1 -> Write 1, Move up, New State 0
State 2, Symbol 2 -> Write 3, Move up, New State 0
State 2, Symbol 3 -> Write 2, Move down, New State 1
State 3, Symbol 0 -> Write 3, Move up, New State 2
State 3, Symbol 1 -> Write 1, Move down, New State 0
State 3, Symbol 2 -> Write 3, Move up, New State 3
State 3, Symbol 3 -> Write 1, Move right, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 0) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 6 steps?
Options:
1: (3, 2)
2: (0, 3)
3: (2, 3)
4: (3, 1)
5: (1, 0)
6: (2, 1)
7: (3, 0)
8: (2, 0)
| 5 | [
"(3, 2)",
"(0, 3)",
"(2, 3)",
"(3, 1)",
"(1, 0)",
"(2, 1)",
"(3, 0)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move up, New State 3
- **Symbol Written on (1, 0):** 0
- **New Position:** (0, 0)
- **New State:** 3
Step 2:
- **Position:** (0, 0)
- **State:** 3
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: <1>
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (0, 0):** 1
- **New Position:** (1, 0)
- **New State:** 0
Step 3:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move up, New State 3
- **Symbol Written on (1, 0):** 0
- **New Position:** (0, 0)
- **New State:** 3
Step 4:
- **Position:** (0, 0)
- **State:** 3
- **Symbol:** According to step 2, it has been changed to symbol 1
- **State and Symbol**: <1>
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (0, 0):** 1
- **New Position:** (1, 0)
- **New State:** 0
Step 5:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move up, New State 3
- **Symbol Written on (1, 0):** 0
- **New Position:** (0, 0)
- **New State:** 3
Step 6:
- **Position:** (0, 0)
- **State:** 3
- **Symbol:** According to step 4, it has been changed to symbol 1
- **State and Symbol**: <1>
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (0, 0):** 1
- **New Position:** (1, 0)
- **New State:** 0
Therefore, the final position after 6 steps will be (1, 0).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00037 | games_images_test/2d_turing_machine/00037.png | states/00037.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move up, New State 3
State 0, Symbol 1 -> Write 0, Move down, New State 3
State 0, Symbol 2 -> Write 2, Move right, New State 1
State 1, Symbol 0 -> Write 1, Move left, New State 0
State 1, Symbol 1 -> Write 0, Move left, New State 0
State 1, Symbol 2 -> Write 2, Move down, New State 2
State 2, Symbol 0 -> Write 2, Move right, New State 2
State 2, Symbol 1 -> Write 2, Move up, New State 1
State 2, Symbol 2 -> Write 1, Move left, New State 3
State 3, Symbol 0 -> Write 2, Move right, New State 0
State 3, Symbol 1 -> Write 2, Move left, New State 3
State 3, Symbol 2 -> Write 1, Move up, New State 3
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 1) with State 1 on Symbol 2 that is [2].
Question: where will the head be after 8 steps?
Options:
1: (2, 0)
2: (2, 2)
3: (2, 1)
4: (0, 1)
5: (1, 1)
6: (0, 0)
7: (1, 0)
8: (0, 2)
| 4 | [
"(2, 0)",
"(2, 2)",
"(2, 1)",
"(0, 1)",
"(1, 1)",
"(0, 0)",
"(1, 0)",
"(0, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move down, New State 2
- **Symbol Written on (0, 1):** 2
- **New Position:** (1, 1)
- **New State:** 2
Step 2:
- **Position:** (1, 1)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 2, Move right, New State 2
- **Symbol Written on (1, 1):** 2
- **New Position:** (1, 2)
- **New State:** 2
Step 3:
- **Position:** (1, 2)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 2, Move up, New State 1
- **Symbol Written on (1, 2):** 2
- **New Position:** (0, 2)
- **New State:** 1
Step 4:
- **Position:** (0, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 1, Move left, New State 0
- **Symbol Written on (0, 2):** 1
- **New Position:** (0, 1)
- **New State:** 0
Step 5:
- **Position:** (0, 1)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (0, 1):** 2
- **New Position:** (0, 2)
- **New State:** 1
Step 6:
- **Position:** (0, 2)
- **State:** 1
- **Symbol:** According to step 4, it has been changed to symbol 1
- **State and Symbol**: [1]
- **Action:** Write 0, Move left, New State 0
- **Symbol Written on (0, 2):** 0
- **New Position:** (0, 1)
- **New State:** 0
Step 7:
- **Position:** (0, 1)
- **State:** 0
- **Symbol:** According to step 5, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (0, 1):** 2
- **New Position:** (0, 2)
- **New State:** 1
Step 8:
- **Position:** (0, 2)
- **State:** 1
- **Symbol:** According to step 6, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 1, Move left, New State 0
- **Symbol Written on (0, 2):** 1
- **New Position:** (0, 1)
- **New State:** 0
Therefore, the final position after 8 steps will be (0, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00038 | games_images_test/2d_turing_machine/00038.png | states/00038.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 3, Move up, New State 1
State 0, Symbol 1 -> Write 0, Move up, New State 3
State 0, Symbol 2 -> Write 1, Move up, New State 0
State 0, Symbol 3 -> Write 2, Move left, New State 2
State 1, Symbol 0 -> Write 0, Move down, New State 2
State 1, Symbol 1 -> Write 0, Move up, New State 2
State 1, Symbol 2 -> Write 2, Move left, New State 1
State 1, Symbol 3 -> Write 1, Move left, New State 3
State 2, Symbol 0 -> Write 3, Move up, New State 0
State 2, Symbol 1 -> Write 3, Move down, New State 1
State 2, Symbol 2 -> Write 2, Move left, New State 1
State 2, Symbol 3 -> Write 1, Move down, New State 1
State 3, Symbol 0 -> Write 0, Move left, New State 1
State 3, Symbol 1 -> Write 2, Move down, New State 3
State 3, Symbol 2 -> Write 3, Move right, New State 2
State 3, Symbol 3 -> Write 1, Move right, New State 3
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (4, 2) with State 1 on Symbol 1 that is [1].
Question: where will the head be after 7 steps?
Options:
1: (3, 2)
2: (2, 1)
3: (4, 2)
4: (4, 1)
5: (0, 0)
6: (3, 0)
7: (1, 2)
8: (0, 2)
| 6 | [
"(3, 2)",
"(2, 1)",
"(4, 2)",
"(4, 1)",
"(0, 0)",
"(3, 0)",
"(1, 2)",
"(0, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (4, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 0, Move up, New State 2
- **Symbol Written on (4, 2):** 0
- **New Position:** (3, 2)
- **New State:** 2
Step 2:
- **Position:** (3, 2)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 3, Move up, New State 0
- **Symbol Written on (3, 2):** 3
- **New Position:** (2, 2)
- **New State:** 0
Step 3:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 3, Move up, New State 1
- **Symbol Written on (2, 2):** 3
- **New Position:** (1, 2)
- **New State:** 1
Step 4:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move left, New State 1
- **Symbol Written on (1, 2):** 2
- **New Position:** (1, 1)
- **New State:** 1
Step 5:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move down, New State 2
- **Symbol Written on (1, 1):** 0
- **New Position:** (2, 1)
- **New State:** 2
Step 6:
- **Position:** (2, 1)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 3, Move down, New State 1
- **Symbol Written on (2, 1):** 3
- **New Position:** (3, 1)
- **New State:** 1
Step 7:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 1, Move left, New State 3
- **Symbol Written on (3, 1):** 1
- **New Position:** (3, 0)
- **New State:** 3
Therefore, the final position after 7 steps will be (3, 0).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00039 | games_images_test/2d_turing_machine/00039.png | states/00039.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move left, New State 1
State 0, Symbol 1 -> Write 3, Move left, New State 1
State 0, Symbol 2 -> Write 1, Move left, New State 0
State 0, Symbol 3 -> Write 1, Move left, New State 1
State 0, Symbol 4 -> Write 0, Move down, New State 3
State 1, Symbol 0 -> Write 2, Move down, New State 2
State 1, Symbol 1 -> Write 3, Move right, New State 1
State 1, Symbol 2 -> Write 1, Move right, New State 3
State 1, Symbol 3 -> Write 2, Move up, New State 1
State 1, Symbol 4 -> Write 4, Move right, New State 0
State 2, Symbol 0 -> Write 4, Move left, New State 2
State 2, Symbol 1 -> Write 2, Move left, New State 0
State 2, Symbol 2 -> Write 0, Move up, New State 3
State 2, Symbol 3 -> Write 1, Move up, New State 3
State 2, Symbol 4 -> Write 3, Move down, New State 2
State 3, Symbol 0 -> Write 2, Move right, New State 0
State 3, Symbol 1 -> Write 2, Move up, New State 1
State 3, Symbol 2 -> Write 3, Move left, New State 1
State 3, Symbol 3 -> Write 0, Move left, New State 1
State 3, Symbol 4 -> Write 1, Move right, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 2) with State 2 on Symbol 1 that is {1}.
Question: where will the head be after 6 steps?
Options:
1: (2, 1)
2: (0, 2)
3: (2, 0)
4: (1, 1)
5: (0, 1)
6: (0, 0)
7: (1, 2)
8: (2, 2)
| 4 | [
"(2, 1)",
"(0, 2)",
"(2, 0)",
"(1, 1)",
"(0, 1)",
"(0, 0)",
"(1, 2)",
"(2, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 2)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 2, Move left, New State 0
- **Symbol Written on (2, 2):** 2
- **New Position:** (2, 1)
- **New State:** 0
Step 2:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move left, New State 1
- **Symbol Written on (2, 1):** 2
- **New Position:** (2, 0)
- **New State:** 1
Step 3:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 1, Move right, New State 3
- **Symbol Written on (2, 0):** 1
- **New Position:** (2, 1)
- **New State:** 3
Step 4:
- **Position:** (2, 1)
- **State:** 3
- **Symbol:** According to step 2, it has been changed to symbol 2
- **State and Symbol**: <2>
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (2, 1):** 3
- **New Position:** (2, 0)
- **New State:** 1
Step 5:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** According to step 3, it has been changed to symbol 1
- **State and Symbol**: [1]
- **Action:** Write 3, Move right, New State 1
- **Symbol Written on (2, 0):** 3
- **New Position:** (2, 1)
- **New State:** 1
Step 6:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** According to step 4, it has been changed to symbol 3
- **State and Symbol**: [3]
- **Action:** Write 2, Move up, New State 1
- **Symbol Written on (2, 1):** 2
- **New Position:** (1, 1)
- **New State:** 1
Therefore, the final position after 6 steps will be (1, 1).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00040 | games_images_test/2d_turing_machine/00040.png | states/00040.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move up, New State 1
State 0, Symbol 1 -> Write 2, Move right, New State 1
State 0, Symbol 2 -> Write 1, Move up, New State 1
State 0, Symbol 3 -> Write 3, Move down, New State 0
State 0, Symbol 4 -> Write 1, Move left, New State 0
State 1, Symbol 0 -> Write 0, Move up, New State 1
State 1, Symbol 1 -> Write 0, Move left, New State 0
State 1, Symbol 2 -> Write 2, Move left, New State 1
State 1, Symbol 3 -> Write 3, Move down, New State 0
State 1, Symbol 4 -> Write 1, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (2, 0) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 3 steps?
Options:
1: (1, 3)
2: (1, 4)
3: (1, 2)
4: (2, 2)
5: (3, 2)
6: (2, 3)
7: (2, 0)
8: (0, 4)
| 5 | [
"(1, 3)",
"(1, 4)",
"(1, 2)",
"(2, 2)",
"(3, 2)",
"(2, 3)",
"(2, 0)",
"(0, 4)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (2, 0):** 2
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 3, Move down, New State 0
- **Symbol Written on (2, 1):** 3
- **New Position:** (3, 1)
- **New State:** 0
Step 3:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (3, 1):** 2
- **New Position:** (3, 2)
- **New State:** 1
Therefore, the final position after 3 steps will be (3, 2).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00041 | games_images_test/2d_turing_machine/00041.png | states/00041.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move left, New State 0
State 0, Symbol 1 -> Write 2, Move right, New State 2
State 0, Symbol 2 -> Write 1, Move left, New State 2
State 1, Symbol 0 -> Write 2, Move up, New State 0
State 1, Symbol 1 -> Write 1, Move up, New State 1
State 1, Symbol 2 -> Write 0, Move left, New State 2
State 2, Symbol 0 -> Write 2, Move up, New State 0
State 2, Symbol 1 -> Write 2, Move down, New State 0
State 2, Symbol 2 -> Write 2, Move right, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 2) with State 1 on Symbol 2 that is [2].
Question: where will the head be after 4 steps?
Options:
1: (0, 2)
2: (1, 1)
3: (1, 0)
4: (0, 1)
5: (2, 2)
6: (3, 2)
7: (3, 1)
8: (3, 0)
| 6 | [
"(0, 2)",
"(1, 1)",
"(1, 0)",
"(0, 1)",
"(2, 2)",
"(3, 2)",
"(3, 1)",
"(3, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 0, Move left, New State 2
- **Symbol Written on (3, 2):** 0
- **New Position:** (3, 1)
- **New State:** 2
Step 2:
- **Position:** (3, 1)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 1):** 2
- **New Position:** (2, 1)
- **New State:** 0
Step 3:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 2, Move right, New State 2
- **Symbol Written on (2, 1):** 2
- **New Position:** (2, 2)
- **New State:** 2
Step 4:
- **Position:** (2, 2)
- **State:** 2
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: {1}
- **Action:** Write 2, Move down, New State 0
- **Symbol Written on (2, 2):** 2
- **New Position:** (3, 2)
- **New State:** 0
Therefore, the final position after 4 steps will be (3, 2).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00042 | games_images_test/2d_turing_machine/00042.png | states/00042.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move left, New State 1
State 0, Symbol 1 -> Write 0, Move right, New State 1
State 0, Symbol 2 -> Write 1, Move up, New State 0
State 1, Symbol 0 -> Write 0, Move down, New State 0
State 1, Symbol 1 -> Write 0, Move left, New State 0
State 1, Symbol 2 -> Write 1, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 2) with State 0 on Symbol 0 that is (0).
Question: where will the head be after 4 steps?
Options:
1: (3, 0)
2: (1, 1)
3: (3, 2)
4: (2, 2)
5: (4, 0)
6: (0, 2)
7: (1, 0)
8: (0, 0)
| 7 | [
"(3, 0)",
"(1, 1)",
"(3, 2)",
"(2, 2)",
"(4, 0)",
"(0, 2)",
"(1, 0)",
"(0, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (3, 2):** 1
- **New Position:** (3, 1)
- **New State:** 1
Step 2:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 0, Move left, New State 0
- **Symbol Written on (3, 1):** 0
- **New Position:** (3, 0)
- **New State:** 0
Step 3:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (3, 0):** 1
- **New Position:** (2, 0)
- **New State:** 0
Step 4:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (2, 0):** 1
- **New Position:** (1, 0)
- **New State:** 0
Therefore, the final position after 4 steps will be (1, 0).
The answer is option 7. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00043 | games_images_test/2d_turing_machine/00043.png | states/00043.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move up, New State 1
State 0, Symbol 1 -> Write 0, Move left, New State 0
State 0, Symbol 2 -> Write 2, Move right, New State 1
State 1, Symbol 0 -> Write 2, Move up, New State 0
State 1, Symbol 1 -> Write 1, Move down, New State 0
State 1, Symbol 2 -> Write 2, Move up, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (1, 0) with State 0 on Symbol 2 that is (2).
Question: where will the head be after 4 steps?
Options:
1: (2, 1)
2: (1, 1)
3: (1, 0)
4: (3, 1)
5: (1, 2)
6: (0, 2)
7: (0, 0)
8: (4, 1)
| 5 | [
"(2, 1)",
"(1, 1)",
"(1, 0)",
"(3, 1)",
"(1, 2)",
"(0, 2)",
"(0, 0)",
"(4, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (1, 0):** 2
- **New Position:** (1, 1)
- **New State:** 1
Step 2:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move up, New State 1
- **Symbol Written on (1, 1):** 2
- **New Position:** (0, 1)
- **New State:** 1
Step 3:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (0, 1):** 1
- **New Position:** (1, 1)
- **New State:** 0
Step 4:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (1, 1):** 2
- **New Position:** (1, 2)
- **New State:** 1
Therefore, the final position after 4 steps will be (1, 2).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00044 | games_images_test/2d_turing_machine/00044.png | states/00044.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move left, New State 1
State 0, Symbol 1 -> Write 3, Move left, New State 0
State 0, Symbol 2 -> Write 0, Move right, New State 1
State 0, Symbol 3 -> Write 2, Move down, New State 1
State 1, Symbol 0 -> Write 3, Move up, New State 0
State 1, Symbol 1 -> Write 0, Move down, New State 0
State 1, Symbol 2 -> Write 1, Move up, New State 0
State 1, Symbol 3 -> Write 1, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (2, 1) with State 0 on Symbol 3 that is (3).
Question: where will the head be after 3 steps?
Options:
1: (2, 2)
2: (3, 1)
3: (1, 2)
4: (4, 2)
5: (2, 0)
6: (3, 0)
7: (0, 1)
8: (3, 2)
| 1 | [
"(2, 2)",
"(3, 1)",
"(1, 2)",
"(4, 2)",
"(2, 0)",
"(3, 0)",
"(0, 1)",
"(3, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (2, 1):** 2
- **New Position:** (3, 1)
- **New State:** 1
Step 2:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (3, 1):** 1
- **New Position:** (2, 1)
- **New State:** 0
Step 3:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 0, Move right, New State 1
- **Symbol Written on (2, 1):** 0
- **New Position:** (2, 2)
- **New State:** 1
Therefore, the final position after 3 steps will be (2, 2).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00045 | games_images_test/2d_turing_machine/00045.png | states/00045.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move right, New State 0
State 0, Symbol 1 -> Write 1, Move right, New State 1
State 0, Symbol 2 -> Write 1, Move left, New State 0
State 0, Symbol 3 -> Write 2, Move up, New State 0
State 1, Symbol 0 -> Write 2, Move up, New State 0
State 1, Symbol 1 -> Write 0, Move down, New State 0
State 1, Symbol 2 -> Write 2, Move up, New State 0
State 1, Symbol 3 -> Write 1, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 1) with State 1 on Symbol 1 that is [1].
Question: where will the head be after 5 steps?
Options:
1: (3, 1)
2: (4, 2)
3: (1, 2)
4: (1, 0)
5: (3, 2)
6: (2, 0)
7: (0, 2)
8: (2, 1)
| 5 | [
"(3, 1)",
"(4, 2)",
"(1, 2)",
"(1, 0)",
"(3, 2)",
"(2, 0)",
"(0, 2)",
"(2, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (3, 1):** 0
- **New Position:** (4, 1)
- **New State:** 0
Step 2:
- **Position:** (4, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move left, New State 0
- **Symbol Written on (4, 1):** 1
- **New Position:** (4, 0)
- **New State:** 0
Step 3:
- **Position:** (4, 0)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 2, Move right, New State 0
- **Symbol Written on (4, 0):** 2
- **New Position:** (4, 1)
- **New State:** 0
Step 4:
- **Position:** (4, 1)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move right, New State 1
- **Symbol Written on (4, 1):** 1
- **New Position:** (4, 2)
- **New State:** 1
Step 5:
- **Position:** (4, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (4, 2):** 2
- **New Position:** (3, 2)
- **New State:** 0
Therefore, the final position after 5 steps will be (3, 2).
The answer is option 5. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00046 | games_images_test/2d_turing_machine/00046.png | states/00046.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move up, New State 2
State 0, Symbol 1 -> Write 1, Move up, New State 3
State 0, Symbol 2 -> Write 4, Move down, New State 0
State 0, Symbol 3 -> Write 3, Move left, New State 1
State 0, Symbol 4 -> Write 3, Move right, New State 1
State 1, Symbol 0 -> Write 0, Move right, New State 0
State 1, Symbol 1 -> Write 2, Move down, New State 2
State 1, Symbol 2 -> Write 2, Move left, New State 0
State 1, Symbol 3 -> Write 4, Move down, New State 3
State 1, Symbol 4 -> Write 3, Move up, New State 0
State 2, Symbol 0 -> Write 0, Move down, New State 3
State 2, Symbol 1 -> Write 1, Move right, New State 0
State 2, Symbol 2 -> Write 1, Move left, New State 2
State 2, Symbol 3 -> Write 4, Move down, New State 0
State 2, Symbol 4 -> Write 1, Move up, New State 0
State 3, Symbol 0 -> Write 2, Move up, New State 2
State 3, Symbol 1 -> Write 4, Move right, New State 3
State 3, Symbol 2 -> Write 3, Move down, New State 2
State 3, Symbol 3 -> Write 4, Move left, New State 2
State 3, Symbol 4 -> Write 2, Move left, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 3) with State 0 on Symbol 3 that is (3).
Question: where will the head be after 8 steps?
Options:
1: (0, 3)
2: (3, 1)
3: (0, 1)
4: (0, 2)
5: (3, 0)
6: (3, 3)
7: (1, 2)
8: (2, 0)
| 6 | [
"(0, 3)",
"(3, 1)",
"(0, 1)",
"(0, 2)",
"(3, 0)",
"(3, 3)",
"(1, 2)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 3)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (3, 3):** 3
- **New Position:** (3, 2)
- **New State:** 1
Step 2:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (3, 2):** 0
- **New Position:** (3, 3)
- **New State:** 0
Step 3:
- **Position:** (3, 3)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (3, 3):** 3
- **New Position:** (3, 2)
- **New State:** 1
Step 4:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** According to step 2, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (3, 2):** 0
- **New Position:** (3, 3)
- **New State:** 0
Step 5:
- **Position:** (3, 3)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (3, 3):** 3
- **New Position:** (3, 2)
- **New State:** 1
Step 6:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** According to step 4, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (3, 2):** 0
- **New Position:** (3, 3)
- **New State:** 0
Step 7:
- **Position:** (3, 3)
- **State:** 0
- **Symbol:** According to step 5, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (3, 3):** 3
- **New Position:** (3, 2)
- **New State:** 1
Step 8:
- **Position:** (3, 2)
- **State:** 1
- **Symbol:** According to step 6, it has been changed to symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (3, 2):** 0
- **New Position:** (3, 3)
- **New State:** 0
Therefore, the final position after 8 steps will be (3, 3).
The answer is option 6. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00047 | games_images_test/2d_turing_machine/00047.png | states/00047.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move down, New State 1
State 0, Symbol 1 -> Write 0, Move down, New State 0
State 0, Symbol 2 -> Write 0, Move down, New State 0
State 1, Symbol 0 -> Write 1, Move up, New State 0
State 1, Symbol 1 -> Write 2, Move left, New State 1
State 1, Symbol 2 -> Write 0, Move up, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 1) with State 1 on Symbol 2 that is [2].
Question: where will the head be after 3 steps?
Options:
1: (3, 2)
2: (3, 1)
3: (2, 1)
4: (3, 0)
5: (4, 1)
6: (1, 1)
7: (0, 3)
8: (3, 3)
| 3 | [
"(3, 2)",
"(3, 1)",
"(2, 1)",
"(3, 0)",
"(4, 1)",
"(1, 1)",
"(0, 3)",
"(3, 3)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 0, Move up, New State 1
- **Symbol Written on (3, 1):** 0
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (2, 1):** 1
- **New Position:** (1, 1)
- **New State:** 0
Step 3:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (1, 1):** 0
- **New Position:** (2, 1)
- **New State:** 0
Therefore, the final position after 3 steps will be (2, 1).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00048 | games_images_test/2d_turing_machine/00048.png | states/00048.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 4, Move left, New State 0
State 0, Symbol 1 -> Write 4, Move left, New State 1
State 0, Symbol 2 -> Write 2, Move right, New State 0
State 0, Symbol 3 -> Write 3, Move down, New State 0
State 0, Symbol 4 -> Write 1, Move up, New State 1
State 1, Symbol 0 -> Write 0, Move left, New State 1
State 1, Symbol 1 -> Write 3, Move up, New State 0
State 1, Symbol 2 -> Write 4, Move right, New State 0
State 1, Symbol 3 -> Write 3, Move left, New State 1
State 1, Symbol 4 -> Write 4, Move down, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (2, 1) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 5 steps?
Options:
1: (1, 1)
2: (1, 2)
3: (3, 1)
4: (2, 1)
5: (3, 0)
6: (0, 1)
7: (2, 2)
8: (0, 2)
| 3 | [
"(1, 1)",
"(1, 2)",
"(3, 1)",
"(2, 1)",
"(3, 0)",
"(0, 1)",
"(2, 2)",
"(0, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 4, Move left, New State 1
- **Symbol Written on (2, 1):** 4
- **New Position:** (2, 0)
- **New State:** 1
Step 2:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: [4]
- **Action:** Write 4, Move down, New State 0
- **Symbol Written on (2, 0):** 4
- **New Position:** (3, 0)
- **New State:** 0
Step 3:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move right, New State 0
- **Symbol Written on (3, 0):** 2
- **New Position:** (3, 1)
- **New State:** 0
Step 4:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 4, Move left, New State 0
- **Symbol Written on (3, 1):** 4
- **New Position:** (3, 0)
- **New State:** 0
Step 5:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move right, New State 0
- **Symbol Written on (3, 0):** 2
- **New Position:** (3, 1)
- **New State:** 0
Therefore, the final position after 5 steps will be (3, 1).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00049 | games_images_test/2d_turing_machine/00049.png | states/00049.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move up, New State 1
State 0, Symbol 1 -> Write 1, Move up, New State 1
State 0, Symbol 2 -> Write 0, Move left, New State 1
State 1, Symbol 0 -> Write 1, Move down, New State 1
State 1, Symbol 1 -> Write 1, Move down, New State 0
State 1, Symbol 2 -> Write 0, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (2, 2) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 4 steps?
Options:
1: (2, 2)
2: (1, 1)
3: (3, 1)
4: (0, 0)
5: (3, 0)
6: (3, 2)
7: (0, 2)
8: (2, 0)
| 1 | [
"(2, 2)",
"(1, 1)",
"(3, 1)",
"(0, 0)",
"(3, 0)",
"(3, 2)",
"(0, 2)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (2, 2):** 1
- **New Position:** (1, 2)
- **New State:** 1
Step 2:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 1, Move down, New State 1
- **Symbol Written on (1, 2):** 1
- **New Position:** (2, 2)
- **New State:** 1
Step 3:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** According to step 1, it has been changed to symbol 1
- **State and Symbol**: [1]
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (2, 2):** 1
- **New Position:** (3, 2)
- **New State:** 0
Step 4:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move up, New State 1
- **Symbol Written on (3, 2):** 1
- **New Position:** (2, 2)
- **New State:** 1
Therefore, the final position after 4 steps will be (2, 2).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00050 | games_images_test/2d_turing_machine/00050.png | states/00050.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 4, Move down, New State 1
State 0, Symbol 1 -> Write 0, Move up, New State 2
State 0, Symbol 2 -> Write 4, Move right, New State 2
State 0, Symbol 3 -> Write 1, Move right, New State 0
State 0, Symbol 4 -> Write 0, Move left, New State 1
State 1, Symbol 0 -> Write 3, Move up, New State 2
State 1, Symbol 1 -> Write 0, Move right, New State 0
State 1, Symbol 2 -> Write 4, Move left, New State 0
State 1, Symbol 3 -> Write 2, Move up, New State 0
State 1, Symbol 4 -> Write 0, Move right, New State 1
State 2, Symbol 0 -> Write 3, Move left, New State 1
State 2, Symbol 1 -> Write 0, Move left, New State 0
State 2, Symbol 2 -> Write 4, Move down, New State 2
State 2, Symbol 3 -> Write 1, Move left, New State 2
State 2, Symbol 4 -> Write 4, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 0) with State 1 on Symbol 4 that is [4].
Question: where will the head be after 3 steps?
Options:
1: (0, 0)
2: (1, 2)
3: (1, 0)
4: (2, 0)
5: (4, 2)
6: (3, 2)
7: (2, 3)
8: (0, 2)
| 7 | [
"(0, 0)",
"(1, 2)",
"(1, 0)",
"(2, 0)",
"(4, 2)",
"(3, 2)",
"(2, 3)",
"(0, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: [4]
- **Action:** Write 0, Move right, New State 1
- **Symbol Written on (2, 0):** 0
- **New Position:** (2, 1)
- **New State:** 1
Step 2:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: [4]
- **Action:** Write 0, Move right, New State 1
- **Symbol Written on (2, 1):** 0
- **New Position:** (2, 2)
- **New State:** 1
Step 3:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: [4]
- **Action:** Write 0, Move right, New State 1
- **Symbol Written on (2, 2):** 0
- **New Position:** (2, 3)
- **New State:** 1
Therefore, the final position after 3 steps will be (2, 3).
The answer is option 7. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00051 | games_images_test/2d_turing_machine/00051.png | states/00051.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move down, New State 2
State 0, Symbol 1 -> Write 1, Move up, New State 2
State 0, Symbol 2 -> Write 2, Move up, New State 0
State 1, Symbol 0 -> Write 2, Move left, New State 0
State 1, Symbol 1 -> Write 1, Move down, New State 3
State 1, Symbol 2 -> Write 0, Move left, New State 0
State 2, Symbol 0 -> Write 0, Move up, New State 0
State 2, Symbol 1 -> Write 1, Move up, New State 2
State 2, Symbol 2 -> Write 2, Move left, New State 0
State 3, Symbol 0 -> Write 1, Move right, New State 1
State 3, Symbol 1 -> Write 0, Move left, New State 3
State 3, Symbol 2 -> Write 0, Move right, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 1) with State 1 on Symbol 2 that is [2].
Question: where will the head be after 3 steps?
Options:
1: (1, 1)
2: (1, 0)
3: (3, 1)
4: (2, 2)
5: (3, 0)
6: (2, 0)
7: (0, 0)
8: (2, 1)
| 2 | [
"(1, 1)",
"(1, 0)",
"(3, 1)",
"(2, 2)",
"(3, 0)",
"(2, 0)",
"(0, 0)",
"(2, 1)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 0, Move left, New State 0
- **Symbol Written on (3, 1):** 0
- **New Position:** (3, 0)
- **New State:** 0
Step 2:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move up, New State 2
- **Symbol Written on (3, 0):** 1
- **New Position:** (2, 0)
- **New State:** 2
Step 3:
- **Position:** (2, 0)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (2, 0):** 0
- **New Position:** (1, 0)
- **New State:** 0
Therefore, the final position after 3 steps will be (1, 0).
The answer is option 2. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00052 | games_images_test/2d_turing_machine/00052.png | states/00052.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 4, Move left, New State 0
State 0, Symbol 1 -> Write 1, Move left, New State 1
State 0, Symbol 2 -> Write 0, Move down, New State 3
State 0, Symbol 3 -> Write 1, Move down, New State 3
State 0, Symbol 4 -> Write 0, Move left, New State 3
State 1, Symbol 0 -> Write 3, Move down, New State 1
State 1, Symbol 1 -> Write 3, Move right, New State 1
State 1, Symbol 2 -> Write 2, Move up, New State 1
State 1, Symbol 3 -> Write 4, Move right, New State 2
State 1, Symbol 4 -> Write 4, Move down, New State 0
State 2, Symbol 0 -> Write 2, Move left, New State 3
State 2, Symbol 1 -> Write 1, Move left, New State 2
State 2, Symbol 2 -> Write 2, Move up, New State 1
State 2, Symbol 3 -> Write 3, Move up, New State 0
State 2, Symbol 4 -> Write 0, Move down, New State 2
State 3, Symbol 0 -> Write 3, Move left, New State 1
State 3, Symbol 1 -> Write 4, Move down, New State 1
State 3, Symbol 2 -> Write 3, Move left, New State 1
State 3, Symbol 3 -> Write 0, Move right, New State 3
State 3, Symbol 4 -> Write 0, Move up, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 3) with State 3 on Symbol 1 that is <1>.
Question: where will the head be after 3 steps?
Options:
1: (3, 4)
2: (3, 2)
3: (1, 1)
4: (4, 0)
5: (4, 1)
6: (0, 2)
7: (2, 3)
8: (3, 3)
| 7 | [
"(3, 4)",
"(3, 2)",
"(1, 1)",
"(4, 0)",
"(4, 1)",
"(0, 2)",
"(2, 3)",
"(3, 3)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 3)
- **State:** 3
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: <1>
- **Action:** Write 4, Move down, New State 1
- **Symbol Written on (1, 3):** 4
- **New Position:** (2, 3)
- **New State:** 1
Step 2:
- **Position:** (2, 3)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move up, New State 1
- **Symbol Written on (2, 3):** 2
- **New Position:** (1, 3)
- **New State:** 1
Step 3:
- **Position:** (1, 3)
- **State:** 1
- **Symbol:** According to step 1, it has been changed to symbol 4
- **State and Symbol**: [4]
- **Action:** Write 4, Move down, New State 0
- **Symbol Written on (1, 3):** 4
- **New Position:** (2, 3)
- **New State:** 0
Therefore, the final position after 3 steps will be (2, 3).
The answer is option 7. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00053 | games_images_test/2d_turing_machine/00053.png | states/00053.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move up, New State 0
State 0, Symbol 1 -> Write 1, Move down, New State 0
State 0, Symbol 2 -> Write 1, Move up, New State 2
State 1, Symbol 0 -> Write 2, Move up, New State 0
State 1, Symbol 1 -> Write 2, Move right, New State 0
State 1, Symbol 2 -> Write 2, Move right, New State 0
State 2, Symbol 0 -> Write 2, Move down, New State 1
State 2, Symbol 1 -> Write 2, Move right, New State 1
State 2, Symbol 2 -> Write 1, Move left, New State 2
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 0) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 8 steps?
Options:
1: (4, 2)
2: (3, 4)
3: (3, 3)
4: (4, 1)
5: (3, 0)
6: (0, 2)
7: (1, 2)
8: (0, 0)
| 1 | [
"(4, 2)",
"(3, 4)",
"(3, 3)",
"(4, 1)",
"(3, 0)",
"(0, 2)",
"(1, 2)",
"(0, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (2, 0):** 1
- **New Position:** (3, 0)
- **New State:** 0
Step 2:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (3, 0):** 1
- **New Position:** (2, 0)
- **New State:** 0
Step 3:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (2, 0):** 1
- **New Position:** (3, 0)
- **New State:** 0
Step 4:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (3, 0):** 1
- **New Position:** (4, 0)
- **New State:** 0
Step 5:
- **Position:** (4, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move up, New State 2
- **Symbol Written on (4, 0):** 1
- **New Position:** (3, 0)
- **New State:** 2
Step 6:
- **Position:** (3, 0)
- **State:** 2
- **Symbol:** According to step 4, it has been changed to symbol 1
- **State and Symbol**: {1}
- **Action:** Write 2, Move right, New State 1
- **Symbol Written on (3, 0):** 2
- **New Position:** (3, 1)
- **New State:** 1
Step 7:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 2, Move right, New State 0
- **Symbol Written on (3, 1):** 2
- **New Position:** (3, 2)
- **New State:** 0
Step 8:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (3, 2):** 1
- **New Position:** (4, 2)
- **New State:** 0
Therefore, the final position after 8 steps will be (4, 2).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00054 | games_images_test/2d_turing_machine/00054.png | states/00054.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move right, New State 1
State 0, Symbol 1 -> Write 1, Move left, New State 1
State 0, Symbol 2 -> Write 2, Move down, New State 1
State 0, Symbol 3 -> Write 1, Move left, New State 1
State 1, Symbol 0 -> Write 0, Move up, New State 0
State 1, Symbol 1 -> Write 3, Move left, New State 1
State 1, Symbol 2 -> Write 2, Move down, New State 0
State 1, Symbol 3 -> Write 2, Move down, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (1, 2) with State 1 on Symbol 0 that is [0].
Question: where will the head be after 5 steps?
Options:
1: (2, 2)
2: (3, 0)
3: (2, 0)
4: (1, 1)
5: (1, 2)
6: (0, 1)
7: (3, 1)
8: (3, 2)
| 3 | [
"(2, 2)",
"(3, 0)",
"(2, 0)",
"(1, 1)",
"(1, 2)",
"(0, 1)",
"(3, 1)",
"(3, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move up, New State 0
- **Symbol Written on (1, 2):** 0
- **New Position:** (0, 2)
- **New State:** 0
Step 2:
- **Position:** (0, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move left, New State 1
- **Symbol Written on (0, 2):** 1
- **New Position:** (0, 1)
- **New State:** 1
Step 3:
- **Position:** (0, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (0, 1):** 2
- **New Position:** (1, 1)
- **New State:** 1
Step 4:
- **Position:** (1, 1)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (1, 1):** 3
- **New Position:** (1, 0)
- **New State:** 1
Step 5:
- **Position:** (1, 0)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 2, Move down, New State 1
- **Symbol Written on (1, 0):** 2
- **New Position:** (2, 0)
- **New State:** 1
Therefore, the final position after 5 steps will be (2, 0).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00055 | games_images_test/2d_turing_machine/00055.png | states/00055.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move up, New State 1
State 0, Symbol 1 -> Write 1, Move up, New State 0
State 0, Symbol 2 -> Write 1, Move down, New State 1
State 0, Symbol 3 -> Write 3, Move right, New State 1
State 1, Symbol 0 -> Write 2, Move left, New State 0
State 1, Symbol 1 -> Write 3, Move right, New State 1
State 1, Symbol 2 -> Write 3, Move left, New State 1
State 1, Symbol 3 -> Write 1, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 0) with State 0 on Symbol 3 that is (3).
Question: where will the head be after 7 steps?
Options:
1: (2, 0)
2: (0, 0)
3: (4, 0)
4: (1, 2)
5: (3, 2)
6: (3, 1)
7: (0, 2)
8: (2, 2)
| 8 | [
"(2, 0)",
"(0, 0)",
"(4, 0)",
"(1, 2)",
"(3, 2)",
"(3, 1)",
"(0, 2)",
"(2, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move right, New State 1
- **Symbol Written on (3, 0):** 3
- **New Position:** (3, 1)
- **New State:** 1
Step 2:
- **Position:** (3, 1)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (3, 1):** 1
- **New Position:** (2, 1)
- **New State:** 0
Step 3:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move up, New State 0
- **Symbol Written on (2, 1):** 1
- **New Position:** (1, 1)
- **New State:** 0
Step 4:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 1, Move down, New State 1
- **Symbol Written on (1, 1):** 1
- **New Position:** (2, 1)
- **New State:** 1
Step 5:
- **Position:** (2, 1)
- **State:** 1
- **Symbol:** According to step 3, it has been changed to symbol 1
- **State and Symbol**: [1]
- **Action:** Write 3, Move right, New State 1
- **Symbol Written on (2, 1):** 3
- **New Position:** (2, 2)
- **New State:** 1
Step 6:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 2, Move left, New State 0
- **Symbol Written on (2, 2):** 2
- **New Position:** (2, 1)
- **New State:** 0
Step 7:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** According to step 5, it has been changed to symbol 3
- **State and Symbol**: (3)
- **Action:** Write 3, Move right, New State 1
- **Symbol Written on (2, 1):** 3
- **New Position:** (2, 2)
- **New State:** 1
Therefore, the final position after 7 steps will be (2, 2).
The answer is option 8. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00056 | games_images_test/2d_turing_machine/00056.png | states/00056.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 2, Move down, New State 0
State 0, Symbol 1 -> Write 1, Move right, New State 3
State 0, Symbol 2 -> Write 2, Move left, New State 0
State 1, Symbol 0 -> Write 0, Move up, New State 2
State 1, Symbol 1 -> Write 0, Move right, New State 2
State 1, Symbol 2 -> Write 0, Move down, New State 0
State 2, Symbol 0 -> Write 1, Move up, New State 3
State 2, Symbol 1 -> Write 0, Move down, New State 0
State 2, Symbol 2 -> Write 0, Move up, New State 2
State 3, Symbol 0 -> Write 2, Move left, New State 1
State 3, Symbol 1 -> Write 1, Move up, New State 2
State 3, Symbol 2 -> Write 2, Move left, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 0) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 7 steps?
Options:
1: (4, 1)
2: (2, 1)
3: (1, 1)
4: (0, 1)
5: (2, 0)
6: (3, 1)
7: (2, 2)
8: (3, 0)
| 3 | [
"(4, 1)",
"(2, 1)",
"(1, 1)",
"(0, 1)",
"(2, 0)",
"(3, 1)",
"(2, 2)",
"(3, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move right, New State 3
- **Symbol Written on (1, 0):** 1
- **New Position:** (1, 1)
- **New State:** 3
Step 2:
- **Position:** (1, 1)
- **State:** 3
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: <2>
- **Action:** Write 2, Move left, New State 0
- **Symbol Written on (1, 1):** 2
- **New Position:** (1, 0)
- **New State:** 0
Step 3:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move right, New State 3
- **Symbol Written on (1, 0):** 1
- **New Position:** (1, 1)
- **New State:** 3
Step 4:
- **Position:** (1, 1)
- **State:** 3
- **Symbol:** According to step 2, it has been changed to symbol 2
- **State and Symbol**: <2>
- **Action:** Write 2, Move left, New State 0
- **Symbol Written on (1, 1):** 2
- **New Position:** (1, 0)
- **New State:** 0
Step 5:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move right, New State 3
- **Symbol Written on (1, 0):** 1
- **New Position:** (1, 1)
- **New State:** 3
Step 6:
- **Position:** (1, 1)
- **State:** 3
- **Symbol:** According to step 4, it has been changed to symbol 2
- **State and Symbol**: <2>
- **Action:** Write 2, Move left, New State 0
- **Symbol Written on (1, 1):** 2
- **New Position:** (1, 0)
- **New State:** 0
Step 7:
- **Position:** (1, 0)
- **State:** 0
- **Symbol:** According to step 5, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move right, New State 3
- **Symbol Written on (1, 0):** 1
- **New Position:** (1, 1)
- **New State:** 3
Therefore, the final position after 7 steps will be (1, 1).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00057 | games_images_test/2d_turing_machine/00057.png | states/00057.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move down, New State 0
State 0, Symbol 1 -> Write 1, Move down, New State 0
State 0, Symbol 2 -> Write 2, Move up, New State 0
State 1, Symbol 0 -> Write 1, Move up, New State 1
State 1, Symbol 1 -> Write 2, Move left, New State 1
State 1, Symbol 2 -> Write 2, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (3, 2) with State 0 on Symbol 2 that is (2).
Question: where will the head be after 5 steps?
Options:
1: (1, 2)
2: (3, 0)
3: (1, 0)
4: (2, 1)
5: (0, 1)
6: (0, 2)
7: (3, 2)
8: (2, 2)
| 8 | [
"(1, 2)",
"(3, 0)",
"(1, 0)",
"(2, 1)",
"(0, 1)",
"(0, 2)",
"(3, 2)",
"(2, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 2):** 2
- **New Position:** (2, 2)
- **New State:** 0
Step 2:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (2, 2):** 1
- **New Position:** (3, 2)
- **New State:** 0
Step 3:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 2):** 2
- **New Position:** (2, 2)
- **New State:** 0
Step 4:
- **Position:** (2, 2)
- **State:** 0
- **Symbol:** According to step 2, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 0
- **Symbol Written on (2, 2):** 1
- **New Position:** (3, 2)
- **New State:** 0
Step 5:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 2):** 2
- **New Position:** (2, 2)
- **New State:** 0
Therefore, the final position after 5 steps will be (2, 2).
The answer is option 8. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00058 | games_images_test/2d_turing_machine/00058.png | states/00058.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 3, Move down, New State 2
State 0, Symbol 1 -> Write 2, Move right, New State 1
State 0, Symbol 2 -> Write 0, Move right, New State 1
State 0, Symbol 3 -> Write 3, Move right, New State 1
State 1, Symbol 0 -> Write 2, Move up, New State 0
State 1, Symbol 1 -> Write 2, Move up, New State 1
State 1, Symbol 2 -> Write 1, Move left, New State 2
State 1, Symbol 3 -> Write 3, Move right, New State 1
State 2, Symbol 0 -> Write 3, Move down, New State 1
State 2, Symbol 1 -> Write 2, Move up, New State 0
State 2, Symbol 2 -> Write 1, Move right, New State 1
State 2, Symbol 3 -> Write 1, Move up, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 1) with State 2 on Symbol 2 that is {2}.
Question: where will the head be after 5 steps?
Options:
1: (1, 1)
2: (0, 1)
3: (2, 2)
4: (0, 2)
5: (2, 1)
6: (1, 2)
7: (1, 0)
8: (2, 0)
| 3 | [
"(1, 1)",
"(0, 1)",
"(2, 2)",
"(0, 2)",
"(2, 1)",
"(1, 2)",
"(1, 0)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 1)
- **State:** 2
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: {2}
- **Action:** Write 1, Move right, New State 1
- **Symbol Written on (2, 1):** 1
- **New Position:** (2, 2)
- **New State:** 1
Step 2:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 1, Move left, New State 2
- **Symbol Written on (2, 2):** 1
- **New Position:** (2, 1)
- **New State:** 2
Step 3:
- **Position:** (2, 1)
- **State:** 2
- **Symbol:** According to step 1, it has been changed to symbol 1
- **State and Symbol**: {1}
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (2, 1):** 2
- **New Position:** (1, 1)
- **New State:** 0
Step 4:
- **Position:** (1, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 3, Move down, New State 2
- **Symbol Written on (1, 1):** 3
- **New Position:** (2, 1)
- **New State:** 2
Step 5:
- **Position:** (2, 1)
- **State:** 2
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: {2}
- **Action:** Write 1, Move right, New State 1
- **Symbol Written on (2, 1):** 1
- **New Position:** (2, 2)
- **New State:** 1
Therefore, the final position after 5 steps will be (2, 2).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00059 | games_images_test/2d_turing_machine/00059.png | states/00059.json | Hard | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move left, New State 0
State 0, Symbol 1 -> Write 3, Move right, New State 1
State 0, Symbol 2 -> Write 3, Move up, New State 1
State 0, Symbol 3 -> Write 3, Move right, New State 0
State 1, Symbol 0 -> Write 0, Move left, New State 1
State 1, Symbol 1 -> Write 3, Move down, New State 1
State 1, Symbol 2 -> Write 3, Move left, New State 1
State 1, Symbol 3 -> Write 1, Move up, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (0, 3) with State 1 on Symbol 1 that is [1].
Question: where will the head be after 3 steps?
Options:
1: (0, 0)
2: (0, 3)
3: (3, 3)
4: (1, 2)
5: (2, 4)
6: (0, 4)
7: (2, 0)
8: (2, 2)
| 8 | [
"(0, 0)",
"(0, 3)",
"(3, 3)",
"(1, 2)",
"(2, 4)",
"(0, 4)",
"(2, 0)",
"(2, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (0, 3)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 3, Move down, New State 1
- **Symbol Written on (0, 3):** 3
- **New Position:** (1, 3)
- **New State:** 1
Step 2:
- **Position:** (1, 3)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (1, 3):** 3
- **New Position:** (1, 2)
- **New State:** 1
Step 3:
- **Position:** (1, 2)
- **State:** 1
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: [1]
- **Action:** Write 3, Move down, New State 1
- **Symbol Written on (1, 2):** 3
- **New Position:** (2, 2)
- **New State:** 1
Therefore, the final position after 3 steps will be (2, 2).
The answer is option 8. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00060 | games_images_test/2d_turing_machine/00060.png | states/00060.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move right, New State 2
State 0, Symbol 1 -> Write 1, Move down, New State 2
State 0, Symbol 2 -> Write 2, Move left, New State 2
State 1, Symbol 0 -> Write 2, Move up, New State 2
State 1, Symbol 1 -> Write 1, Move down, New State 1
State 1, Symbol 2 -> Write 0, Move up, New State 2
State 2, Symbol 0 -> Write 2, Move up, New State 0
State 2, Symbol 1 -> Write 0, Move down, New State 0
State 2, Symbol 2 -> Write 0, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 1) with State 0 on Symbol 2 that is (2).
Question: where will the head be after 7 steps?
Options:
1: (0, 1)
2: (1, 2)
3: (3, 1)
4: (3, 0)
5: (0, 0)
6: (2, 2)
7: (2, 1)
8: (2, 0)
| 4 | [
"(0, 1)",
"(1, 2)",
"(3, 1)",
"(3, 0)",
"(0, 0)",
"(2, 2)",
"(2, 1)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move left, New State 2
- **Symbol Written on (3, 1):** 2
- **New Position:** (3, 0)
- **New State:** 2
Step 2:
- **Position:** (3, 0)
- **State:** 2
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: {0}
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 0):** 2
- **New Position:** (2, 0)
- **New State:** 0
Step 3:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 2
- **Symbol Written on (2, 0):** 1
- **New Position:** (3, 0)
- **New State:** 2
Step 4:
- **Position:** (3, 0)
- **State:** 2
- **Symbol:** According to step 2, it has been changed to symbol 2
- **State and Symbol**: {2}
- **Action:** Write 0, Move right, New State 0
- **Symbol Written on (3, 0):** 0
- **New Position:** (3, 1)
- **New State:** 0
Step 5:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** According to step 1, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 2, Move left, New State 2
- **Symbol Written on (3, 1):** 2
- **New Position:** (3, 0)
- **New State:** 2
Step 6:
- **Position:** (3, 0)
- **State:** 2
- **Symbol:** According to step 4, it has been changed to symbol 0
- **State and Symbol**: {0}
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 0):** 2
- **New Position:** (2, 0)
- **New State:** 0
Step 7:
- **Position:** (2, 0)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 1
- **State and Symbol**: (1)
- **Action:** Write 1, Move down, New State 2
- **Symbol Written on (2, 0):** 1
- **New Position:** (3, 0)
- **New State:** 2
Therefore, the final position after 7 steps will be (3, 0).
The answer is option 4. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00061 | games_images_test/2d_turing_machine/00061.png | states/00061.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 1, Move down, New State 0
State 0, Symbol 1 -> Write 4, Move up, New State 1
State 0, Symbol 2 -> Write 3, Move up, New State 0
State 0, Symbol 3 -> Write 2, Move right, New State 1
State 0, Symbol 4 -> Write 1, Move left, New State 0
State 1, Symbol 0 -> Write 4, Move right, New State 2
State 1, Symbol 1 -> Write 3, Move down, New State 3
State 1, Symbol 2 -> Write 0, Move up, New State 1
State 1, Symbol 3 -> Write 3, Move left, New State 3
State 1, Symbol 4 -> Write 4, Move left, New State 2
State 2, Symbol 0 -> Write 0, Move right, New State 2
State 2, Symbol 1 -> Write 3, Move down, New State 3
State 2, Symbol 2 -> Write 2, Move down, New State 3
State 2, Symbol 3 -> Write 3, Move down, New State 0
State 2, Symbol 4 -> Write 1, Move right, New State 3
State 3, Symbol 0 -> Write 0, Move right, New State 2
State 3, Symbol 1 -> Write 1, Move left, New State 3
State 3, Symbol 2 -> Write 2, Move right, New State 0
State 3, Symbol 3 -> Write 0, Move down, New State 0
State 3, Symbol 4 -> Write 2, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (3, 2) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 3 steps?
Options:
1: (1, 1)
2: (1, 0)
3: (3, 0)
4: (4, 0)
5: (4, 2)
6: (2, 1)
7: (0, 2)
8: (2, 0)
| 1 | [
"(1, 1)",
"(1, 0)",
"(3, 0)",
"(4, 0)",
"(4, 2)",
"(2, 1)",
"(0, 2)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (3, 2)
- **State:** 0
- **Symbol:** Directly from image, it's green which means symbol 1
- **State and Symbol**: (1)
- **Action:** Write 4, Move up, New State 1
- **Symbol Written on (3, 2):** 4
- **New Position:** (2, 2)
- **New State:** 1
Step 2:
- **Position:** (2, 2)
- **State:** 1
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: [3]
- **Action:** Write 3, Move left, New State 3
- **Symbol Written on (2, 2):** 3
- **New Position:** (2, 1)
- **New State:** 3
Step 3:
- **Position:** (2, 1)
- **State:** 3
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: <4>
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (2, 1):** 2
- **New Position:** (1, 1)
- **New State:** 0
Therefore, the final position after 3 steps will be (1, 1).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00062 | games_images_test/2d_turing_machine/00062.png | states/00062.json | Medium | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 0, Move down, New State 0
State 0, Symbol 1 -> Write 1, Move right, New State 0
State 0, Symbol 2 -> Write 3, Move left, New State 1
State 0, Symbol 3 -> Write 2, Move up, New State 0
State 1, Symbol 0 -> Write 0, Move left, New State 0
State 1, Symbol 1 -> Write 0, Move up, New State 0
State 1, Symbol 2 -> Write 0, Move down, New State 1
State 1, Symbol 3 -> Write 1, Move left, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
Current head position is (4, 2) with State 1 on Symbol 0 that is [0].
Question: where will the head be after 5 steps?
Options:
1: (3, 0)
2: (2, 1)
3: (0, 0)
4: (1, 1)
5: (0, 2)
6: (4, 1)
7: (3, 1)
8: (3, 2)
| 1 | [
"(3, 0)",
"(2, 1)",
"(0, 0)",
"(1, 1)",
"(0, 2)",
"(4, 1)",
"(3, 1)",
"(3, 2)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (4, 2)
- **State:** 1
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: [0]
- **Action:** Write 0, Move left, New State 0
- **Symbol Written on (4, 2):** 0
- **New Position:** (4, 1)
- **New State:** 0
Step 2:
- **Position:** (4, 1)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (4, 1):** 2
- **New Position:** (3, 1)
- **New State:** 0
Step 3:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: (3)
- **Action:** Write 2, Move up, New State 0
- **Symbol Written on (3, 1):** 2
- **New Position:** (2, 1)
- **New State:** 0
Step 4:
- **Position:** (2, 1)
- **State:** 0
- **Symbol:** Directly from image, it's red which means symbol 0
- **State and Symbol**: (0)
- **Action:** Write 0, Move down, New State 0
- **Symbol Written on (2, 1):** 0
- **New Position:** (3, 1)
- **New State:** 0
Step 5:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** According to step 3, it has been changed to symbol 2
- **State and Symbol**: (2)
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (3, 1):** 3
- **New Position:** (3, 0)
- **New State:** 1
Therefore, the final position after 5 steps will be (3, 0).
The answer is option 1. | 2d_turing_machine | Multi-step Reasoning | null | null |
turing-machine-test-00063 | games_images_test/2d_turing_machine/00063.png | states/00063.json | Easy | State Prediction | Medium | 0 | position | Rules:
State 0, Symbol 0 -> Write 4, Move right, New State 3
State 0, Symbol 1 -> Write 4, Move down, New State 3
State 0, Symbol 2 -> Write 3, Move right, New State 0
State 0, Symbol 3 -> Write 1, Move right, New State 3
State 0, Symbol 4 -> Write 1, Move up, New State 2
State 1, Symbol 0 -> Write 1, Move right, New State 1
State 1, Symbol 1 -> Write 0, Move down, New State 0
State 1, Symbol 2 -> Write 4, Move down, New State 0
State 1, Symbol 3 -> Write 3, Move left, New State 1
State 1, Symbol 4 -> Write 0, Move up, New State 1
State 2, Symbol 0 -> Write 4, Move up, New State 3
State 2, Symbol 1 -> Write 3, Move down, New State 1
State 2, Symbol 2 -> Write 3, Move up, New State 3
State 2, Symbol 3 -> Write 3, Move left, New State 1
State 2, Symbol 4 -> Write 4, Move right, New State 0
State 3, Symbol 0 -> Write 1, Move right, New State 1
State 3, Symbol 1 -> Write 4, Move right, New State 2
State 3, Symbol 2 -> Write 3, Move down, New State 0
State 3, Symbol 3 -> Write 0, Move left, New State 2
State 3, Symbol 4 -> Write 4, Move right, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (2, 1) with State 2 on Symbol 3 that is {3}.
Question: where will the head be after 4 steps?
Options:
1: (1, 0)
2: (2, 2)
3: (2, 1)
4: (1, 1)
5: (3, 1)
6: (3, 2)
7: (3, 0)
8: (2, 0)
| 3 | [
"(1, 0)",
"(2, 2)",
"(2, 1)",
"(1, 1)",
"(3, 1)",
"(3, 2)",
"(3, 0)",
"(2, 0)"
] | Detailed step-by-step analysis:
Step 1:
- **Position:** (2, 1)
- **State:** 2
- **Symbol:** Directly from image, it's magenta which means symbol 3
- **State and Symbol**: {3}
- **Action:** Write 3, Move left, New State 1
- **Symbol Written on (2, 1):** 3
- **New Position:** (2, 0)
- **New State:** 1
Step 2:
- **Position:** (2, 0)
- **State:** 1
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: [2]
- **Action:** Write 4, Move down, New State 0
- **Symbol Written on (2, 0):** 4
- **New Position:** (3, 0)
- **New State:** 0
Step 3:
- **Position:** (3, 0)
- **State:** 0
- **Symbol:** Directly from image, it's blue which means symbol 2
- **State and Symbol**: (2)
- **Action:** Write 3, Move right, New State 0
- **Symbol Written on (3, 0):** 3
- **New Position:** (3, 1)
- **New State:** 0
Step 4:
- **Position:** (3, 1)
- **State:** 0
- **Symbol:** Directly from image, it's cyan which means symbol 4
- **State and Symbol**: (4)
- **Action:** Write 1, Move up, New State 2
- **Symbol Written on (3, 1):** 1
- **New Position:** (2, 1)
- **New State:** 2
Therefore, the final position after 4 steps will be (2, 1).
The answer is option 3. | 2d_turing_machine | Multi-step Reasoning | null | null |
End of preview.
1. Overview
GameQA is a large-scale, diverse, and challenging multimodal reasoning dataset designed to enhance the general reasoning capabilities of Vision Language Models (VLMs). Generated using the innovative Code2Logic framework, it leverages game code to synthesize high-quality visual-language Chain-of-Thought (CoT) data. The dataset addresses the scarcity of multimodal reasoning data, critical for advancing complex multi-step reasoning in VLMs. Each sample includes visual game states, targeted questions, step-by-step reasoning, and final answers, derived from the logical structures inherent in game code.
2. Dataset Description
| Attribute | Description |
|---|---|
| Size | ~140,000 question-answer pairs (126,760 training, 15,047 testing). |
| Diversity | 30 unique games, 158 distinct tasks covering various cognitive skills. |
| Game Categories | - 3D Spatial Perception and Understanding - Pattern Recognition and Matching - Multi-step Reasoning - Strategic Planning |
| Format | Visual Question Answering (VQA): - Game state image - Targeted question - Step-by-step reasoning - Final answer |
| Question Types | - Multiple-choice (7-8 options) - Fill-in-the-blank (e.g., numbers, coordinates) |
| Challenging | Difficult for SOTA VLMs (<50% accuracy on test set). |
| Scalability & Cost | Code2Logic enables massive-scale generation with minimal cost after initial setup. |
| Difficulty Levels | - Plot Level (Image Complexity): Easy, Medium, Hard - QA Level (Task Complexity): Easy, Medium, Hard |
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