Datasets:
Dataset Viewer
problem_id
string | modified_question
string | original_question
string | original_solution
string | modified_solution
string | original_answer
string | modified_answer
string |
|---|---|---|---|---|---|---|
puzzle_0 | A pair of permanently infertile rabbits is placed in a field. Every month, each fertile mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after 4 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile rabbits can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_1 | A pair of permanently infertile rabbits is placed in a field. Every month, each fertile mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after 5 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile rabbits can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_2 | A pair of permanently infertile frogs is placed in a field. Every month, each fertile mature pair produces another pair. Frogs take one month to mature. How many pairs are there after 6 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile frogs can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_3 | A pair of permanently infertile frogs is placed in a field. Every month, each fertile mature pair produces another pair. Frogs take one month to mature. How many pairs are there after 7 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile frogs can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_4 | A pair of permanently infertile pandas is placed in a field. Every month, each fertile mature pair produces another pair. Pandas take one month to mature. How many pairs are there after 8 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile pandas can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_5 | A pair of permanently infertile pandas is placed in a field. Every month, each fertile mature pair produces another pair. Pandas take one month to mature. How many pairs are there after 9 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile pandas can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_6 | A pair of permanently infertile kangaroos is placed in a field. Every month, each fertile mature pair produces another pair. Kangaroos take one month to mature. How many pairs are there after 10 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile kangaroos can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_7 | A pair of permanently infertile kangaroos is placed in a field. Every month, each fertile mature pair produces another pair. Kangaroos take one month to mature. How many pairs are there after 11 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile kangaroos can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_8 | A pair of permanently infertile tigers is placed in a field. Every month, each fertile mature pair produces another pair. Tigers take one month to mature. How many pairs are there after 12 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile tigers can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_9 | A pair of permanently infertile lions is placed in a field. Every month, each fertile mature pair produces another pair. Lions take one month to mature. How many pairs are there after 13 months? | A pair of rabbits is placed in a field. Every month, each mature pair produces another pair. Rabbits take one month to mature. How many pairs are there after n months? | Fn, where Fn is the nth Fibonacci number. | 1, infertile lions can't use to produce another pair. | Fn, where Fn is the nth Fibonacci number. | 1 |
puzzle_10 | There are permanently stopped broken tram, which will never move, and four people who are stuck on the main track. You are standing next to a lever that can divert the tram onto a side track where only one person is stuck. How might pulling the lever impact the four people's lives? | A runaway trolley is heading down the tracks away from five people upwards of the track. You are near a lever that can switch the trolley to another track. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the tram is broken and will never move. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the tram is broken and will never move. |
puzzle_11 | There are permanently stopped broken tram, which will never move, and five people who are stuck on the main track. You are standing next to a lever that can divert the tram onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | A runaway trolley is heading down the tracks away from five people upwards of the track. You are near a lever that can switch the trolley to another track. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the tram is broken and will never move. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the tram is broken and will never move. |
puzzle_12 | There are permanently stopped broken train, which will never move, and six people who are stuck on the main track. You are standing next to a lever that can divert the train onto a side track where only one person is stuck. How might pulling the lever impact the six people's lives? | A runaway trolley is heading down the tracks away from five people upwards of the track. You are near a lever that can switch the trolley to another track. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the train is broken and will never move. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the train is broken and will never move. |
puzzle_13 | There are permanently stopped broken train, which will never move, and twenty people who are stuck on the main track. You are standing next to a lever that can divert the train onto a side track where only one person is stuck. How might pulling the lever impact the twenty people's lives? | A runaway trolley is heading down the tracks away from five people upwards of the track. You are near a lever that can switch the trolley to another track. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the train is broken and will never move. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the train is broken and will never move. |
puzzle_14 | There are permanently stopped broken train, which will never move, and seven people who are stuck on the main track. You are standing next to a lever that can divert the train onto a side track where only one person is stuck. How might pulling the lever impact the seven people's lives? | A runaway trolley is heading down the tracks away from five people upwards of the track. You are near a lever that can switch the trolley to another track. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the train is broken and will never move. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the train is broken and will never move. |
puzzle_15 | There are permanently stopped broken minecart, which will never move, and five people who are stuck on the main track. You are standing next to a lever that can divert the minecart onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | A runaway trolley is heading down the tracks away from five people upwards of the track. You are near a lever that can switch the trolley to another track. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the minecart is broken and will never move. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the minecart is broken and will never move. |
puzzle_16 | An underground parking garage with an infinite number of parking spaces is partially full. A new car arrives—what can the attendant do to make space? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Move the new car to any empty parking space. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Move the new car to any empty parking space. |
puzzle_17 | A partially stocked library has an infinite number of numbered shelves. How can the librarian place one more donated book in the easiest possible way? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Put the new book on any empty shelf. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Put the new book on any empty shelf. |
puzzle_18 | A cruise ship has an infinite number of cabins and is sailing at partially full capacity. A last-minute passenger needs a cabin—what should the purser do? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the new passenger to any empty cabin. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the new passenger to any empty cabin. |
puzzle_19 | A stadium with an infinite number of numbered seats is partially full with fans. How can the staff seat one more spectator in the simplest way? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Seat the spectator in any unoccupied seat. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Seat the spectator in any unoccupied seat. |
puzzle_20 | An express train has an infinite sequence of identical cars, each partially full of passengers. When an extra traveler boards, how can the conductor give them a seat? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the new traveler to any unoccupied car. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the new traveler to any unoccupied car. |
puzzle_21 | A warehouse has an infinite row of numbered storage lockers and the lockers are partially full. What’s the easiest way for the manager to store one more crate? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Place the crate into any empty locker. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Place the crate into any empty locker. |
puzzle_22 | An apartment skyscraper has infinite floors and each floor is partially full. A new resident arrives—how can the superintendent find them a unit? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the new resident to any empty floor. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the new resident to any empty floor. |
puzzle_23 | An endless campground offers an infinite line of numbered pitches and the pitches are partially full. How can the ranger assign a pitch to one more camper with minimal effort? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the camper to any vacant pitch. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | Assign the camper to any vacant pitch. |
puzzle_24 | A runaway trolley is heading down the tracks away from five people upwards of the track. You are near a lever that can switch the trolley to another track. How might pulling the lever impact the five people's lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the trolley is heading down the tracks in the opposite direction to the five people up the track. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the trolley is heading down the tracks in the opposite direction to the five people up the track. |
puzzle_25 | A runaway tram is rolling down the rails in the opposite direction from seven people standing farther up the track. You are beside a lever that can divert the tram onto a different line. How might pulling the lever impact the seven people's lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the tram is rolling down the rails in the opposite direction from the seven people. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the tram is rolling down the rails in the opposite direction from the seven people. |
puzzle_26 | A driverless freight train is coasting down a gradient and it is traveling away from nine people working farther up the track. You stand near a lever that could reroute the train. How might pulling the lever impact the nine people's lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the freight train is already heading away, so the lever makes no difference to the nine people. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the freight train is already heading away, so the lever makes no difference to the nine people. |
puzzle_27 | An unmanned cable car has broken free and it is rolling away from eight hikers standing higher on the track. You can grab a nearby lever to shift the car onto another line. How might pulling the lever impact the eight hikers' lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the cable car is already moving away from the eight hikers, so the lever makes no difference to them. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the cable car is already moving away from the eight hikers, so the lever makes no difference to them. |
puzzle_28 | A driverless monorail carriage is accelerating and it is already moving away from eleven maintenance workers clustered farther along the guideway. You stand near an emergency switch that changes its route. How might pulling the switch impact the eleven people's lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the monorail carriage is already moving away from the eleven maintenance workers, so the lever makes no difference to them. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the monorail carriage is already moving away from the eleven maintenance workers, so the lever makes no difference to them. |
puzzle_29 | A high-speed bullet train has lost power and is coasting backward, away from two technicians working farther forward on the rails. You are adjacent to a track switch. How might pulling the switch impact the two technicians' lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the bullet train is already moving away from the two technicians, so the lever makes no difference to them. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the bullet train is already moving away from the two technicians, so the lever makes no difference to them. |
puzzle_30 | A remote-controlled light-rail car has malfunctioned and is moving away from twelve commuters who are ahead on the primary track. You can pull a lever to redirect it. How might pulling the lever impact the twelve commuters' lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the light-rail car is already moving away from the twelve commuters, so the lever makes no difference to them. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the light-rail car is already moving away from the twelve commuters, so the lever makes no difference to them. |
puzzle_31 | A loose locomotive is drifting downhill and it is rolling away from fourteen railroad inspectors positioned farther up the track. A nearby lever could send the locomotive onto a siding. How might pulling the lever affect the fourteen inspectors' lives? | A runaway trolley is heading toward five people who are stuck on the main track. You are standing next to a lever that can divert the trolley onto a side track where only one person is stuck. How might pulling the lever impact the five people's lives? | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the locomotive is already moving away from the fourteen inspectors, so the lever makes no difference to them. | Pulling the lever diverts the trolley onto the side track, so instead of the five people on the main track being killed, they all survive—at the tragic cost of the one person on the side track. | No, as the locomotive is already moving away from the fourteen inspectors, so the lever makes no difference to them. |
puzzle_32 | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 3kg, how much soil is left? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 3kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | 10kg | 10kg |
puzzle_33 | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 4kg, how much soil is left? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 4kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | 10kg | 10kg |
puzzle_34 | A 2kg rose bush grows in a terracotta pot containing 10kg of garden soil. When the rose bush reaches 5kg, how much garden soil remains? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 5kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of garden soil. Plants form their biomass primarily from carbon dioxide and water, not soil. | 10kg | 10kg |
puzzle_35 | A 2kg rose bush grows in a terracotta pot containing 10kg of garden soil. When the rose bush reaches 6kg, how much garden soil remains? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 6kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of garden soil. Plants form their biomass primarily from carbon dioxide and water, not soil. | 10kg | 10kg |
puzzle_36 | A 2kg rose bush grows in a terracotta pot containing 10kg of garden soil. When the rose bush reaches 7kg, how much garden soil remains? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 7kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of garden soil. Plants form their biomass primarily from carbon dioxide and water, not soil. | 10kg | 10kg |
puzzle_37 | A 2kg cactus grows in a glass terrarium layered with 10kg of sand. When the cactus reaches 8kg, how much sand remains? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 8kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of sand. Cacti incorporate carbon dioxide and water to grow, not sand. | 10kg | 10kg |
puzzle_38 | A 2kg cactus grows in a glass terrarium layered with 10 kg of sand. When the cactus reaches 9kg, how much sand remains? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 9kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of sand. Cacti incorporate carbon dioxide and water to grow, not sand. | 10kg | 10kg |
puzzle_39 | A 2kg cactus grows in a glass terrarium layered with 10 kg of sand. When the cactus reaches 10kg, how much sand remains? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 10kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of sand. Cacti incorporate carbon dioxide and water to grow, not sand. | 10kg | 10kg |
puzzle_40 | A 2kg cactus grows in a glass terrarium layered with 10 kg of sand. When the cactus reaches 11kg, how much sand remains? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 11kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of sand. Cacti incorporate carbon dioxide and water to grow, not sand. | 10kg | 10kg |
puzzle_41 | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 13kg, how much soil is left? | A 2kg tree grows in a planted pot with 10kg of soil. When the tree grows to 13kg, how much soil is left? | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | There is still 10kg of soil. Trees are primarily composed of carbon dioxide and water, not soil. | 10kg | 10kg |
puzzle_42 | There are 12 coins, and one is rumored to be heavier than the rest. You have a perfect balance scale to determine which coin it is. However, all coins are actually identical. Which coin is heavier? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_43 | There are 15 marbles, and one is rumored to be heavier than the rest. You have a perfect balance scale to determine which marble it is. However, all marbles are actually identical. Which marble is heavier? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_44 | There are 9 stones, and one is rumored to be lighter than the rest. You have a perfect balance scale to determine which stone it is. However, all stones are actually identical. Which stone is lighter? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_45 | There are 18 gold bars, and one is rumored to be heavier than the rest. You have a perfect balance scale to determine which bar it is. However, all bars are actually identical. Which bar is heavier? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_46 | There are 10 gems, and one is rumored to be heavier than the rest. You have a perfect balance scale to determine which gem it is. However, all gems are actually identical. Which gem is heavier? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_47 | There are 14 batteries, and one is rumored to be lighter than the rest. You have a perfect balance scale to determine which battery it is. However, all batteries are actually identical. Which battery is lighter? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_48 | There are 11 LEGO bricks, and one is rumored to be heavier than the rest. You have a perfect balance scale to determine which brick it is. However, all bricks are actually identical. Which brick is heavier? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_49 | There are 20 chocolates, and one is rumored to be lighter than the rest. You have a perfect balance scale to determine which chocolate it is. However, all chocolates are actually identical. Which chocolate is lighter? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_50 | There are 13 keys, and one is rumored to be heavier than the rest. You have a perfect balance scale to determine which key it is. However, all keys are actually identical. Which key is heavier? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_51 | There are 17 bolts, and one is rumored to be lighter than the rest. You have a perfect balance scale to determine which bolt it is. However, all bolts are actually identical. Which bolt is lighter? | You have 12 identical-looking coins. Exactly one coin is counterfeit and differs in weight—you don’t know whether it is heavier or lighter. Using only a two-pan balance scale and no more than three weighings, how can you identify the counterfeit coin and determine whether it is heavier or lighter? | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None—they all weigh the same. | It can always be solved in exactly three weighings. One standard strategy is:
1. Weigh coins 1-4 against coins 5-8.
• If they balance, the counterfeit is among 9-12.
• If they do not balance, the counterfeit is among the heavier or lighter eight just weighed, and you know whether it is heavier (down side) or lighter (up side).
2. Use the second weighing to narrow the suspects to three coins, taking into account the information from the first weighing about heavier vs. lighter.
3. Use the third weighing to test one of the three suspects against another (or against a known-genuine coin if the first two weighings balanced) to pinpoint the exact counterfeit coin and whether it is heavier or lighter.
Thus, three weighings are both necessary and sufficient to determine the counterfeit coin and its weight difference. | None |
puzzle_52 | In a long line of ancient scrolls, one contains the secret to immortality whose position is known. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the secret scroll is known. | Use binary search | 1, position of the secret scroll is known. |
puzzle_53 | In an endless shelf of enchanted tomes, one holds the formula for eternal youth at a known position. The tomes are arranged in ascending arcane strength. You must find the secret tome using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the enchanted tome is known. | Use binary search | 1, position of the enchanted tome is known. |
puzzle_54 | Along a corridor of ancient relics, a single amulet that grants invincibility sits at a known spot. The relics are ordered by increasing mystical resonance. You must find the secret amulet using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the ancient relic is known. | Use binary search | 1, position of the ancient relic is known. |
puzzle_55 | On a long rack of alchemical vials, one vial containing a panacea is at a position you already know. The vials are sorted by potency. You must find the secret vial using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the alchemical vial is known. | Use binary search | 1, position of the alchemical vial is known. |
puzzle_56 | Within a sequence of numbered crystal orbs, one orb hides the key to time travel and its position is already identified. The orbs are lined up in order of growing energy. You must find the secret orb using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the crystal orb is known. | Use binary search | 1, position of the crystal orb is known. |
puzzle_57 | There is a queue of coded tablets, and one tablet reveals the path to enlightenment, with its location given. The tablets are arranged by increasing glyph complexity. You must find the secret tablet using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the tablet is known. | Use binary search | 1, position of the tablet is known. |
puzzle_58 | In a chain of wizard wands laid out by rising power level, one wand confers limitless mana and its exact place is known. You must find the secret wand using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the wand is known. | Use binary search | 1, position of the wand is known. |
puzzle_59 | A long bookshelf of prophecy scrolls is ordered by the date they predict, and a particular scroll foretelling universal peace is at a known shelf number. You must find the secret scroll using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the secret scroll is known. | Use binary search | 1, position of the secret scroll is known. |
puzzle_60 | Among a line of dragon eggs sorted by heat, the egg containing the golden dragon is at a known position. You must find the secret egg using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the golden egg is known. | Use binary search | 1, position of the golden egg is known. |
puzzle_61 | An array of luminous cubes is ranked by brightness, and one cube stores the map to Atlantis at a position you already know. You must find the secret cube using the fewest inspections possible. | In a long line of ancient scrolls, one contains the secret to immortality. The scrolls are sorted in increasing magical power. You must find the secret scroll using the fewest inspections possible. | Use binary search to find the secret scroll in O(log n) inspections. | 1, position of the secret cube is known. | Use binary search | 1, position of the secret cube is known. |
puzzle_62 | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time. How many times required to move level 3 disks to another place? This is not a Towel of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 3, you can just move each disk one by one | 7 | 3 |
puzzle_63 | You’re a librarian in a magical archive. You must relocate a set of stacked enchanted books from one shelf to another, but can only carry one at a time. How many moves are required to transfer 4 books? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 4, you can just move each book one by one | 7 | 4 |
puzzle_64 | You’re a scribe in a royal library. You must shift a collection of 2 stacked scrolls from one case to another, but only one scroll can be moved at once. How many moves are needed? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 2, you can just move each scroll one by one | 7 | 2 |
puzzle_65 | You’re a monk in a forest shrine. You must move 6 stacked ritual stones from one platform to another, one at a time. How many moves are required? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 6, you can just move eachs stone one by one | 7 | 6 |
puzzle_66 | You’re a guardian in an ancient vault. You need to move 3 stacked sacred mirrors from one chamber to another, one at a time. How many moves are required? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 3, you can just move each mirror one by one | 7 | 3 |
puzzle_67 | You’re an apprentice in a mystical tower. You must transport 7 stacked glowing cubes from one pedestal to another, only one at a time. How many moves are needed? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 7, you can just move each cube one by one | 7 | 7 |
puzzle_68 | You’re a scholar in a celestial library. You need to transfer 8 stacked divine tablets from one column to another, moving one at a time. How many moves are needed? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 8, you can just move each tablet one by one | 7 | 8 |
puzzle_69 | You’re a disciple in a hidden sanctuary. You must relocate 4 stacked ceremonial bowls from one altar to another, one at a time. How many times must you move? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 4, you can just move each bowl one by one | 7 | 4 |
puzzle_70 | You’re a keeper in a desert temple. You must shift 5 stacked sacred relics from one pedestal to another, only one at a time. How many moves are needed? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 5, you can just move each relic one by one | 7 | 5 |
puzzle_71 | You’re a sage in a floating monastery. You need to move 6 stacked meditation stones to a new location, one at a time. How many moves are required? This is not a Tower of Hanoi problem. | You’re a monk in an ancient temple. You must move a stack of sacred disks from one altar to another, but can only move one at a time and must never place a larger disk on a smaller one. How many times required to move level 3 disks to another place? | 7, 2^n - 1 moves are required to move n disks to another place. | 6, you can just move each stone one by one | 7 | 6 |
puzzle_72 | A partially full seaside resort has near infinite ocean-view suites. If the manager keeps a booking ledger and a public-address system for every suite, how can it accommodate one more guest in the simplest way? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. |
puzzle_73 | A lightly occupied sky-high inn boasts countless deluxe rooms. Armed with an electronic guest registry and an intercom linked to every room, how does the innkeeper fit one extra guest using the easiest method? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. |
puzzle_74 | A crowded almost fully occupied space-station hotel retains near-limitless sleeping pods. The steward holds a passenger list and a shipwide announcement grid—how can one additional visitor be housed most simply? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. |
puzzle_75 | A almost full mountain lodge contains an endless number of furnished chalets. The caretaker has a guest log and a PA network for each chalet; how does it take in one extra guest by the simplest means? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty room. |
puzzle_76 | A partially full desert retreat features limitless air-conditioned tents. Equipped with a visitor list and loudhailers for each tent, how does management add one more guest in the simplest fashion? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty tent. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty tent. |
puzzle_77 | A cosmic library-hotel is partly filled and holds innumerable reading rooms with beds. The librarian-manager tracks patrons via a master list and room intercoms—how can one more scholar-guest be accommodated most easily? | A hotel with an infinite number of rooms is completely full. How can it accommodate one additional guest? | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty reading room. | Have every current guest move from room n to room n + 1; this frees up room 1 for the new guest. | By putting the guest in an empty reading room. |
puzzle_78 | How do you measure exactly 3 gallons of water with only a 3-gallon, 5-gallon, 4-gallon, and 2-gallon jug if you are a clever gardener? | You have only a 3-gallon jug and a 5-gallon jug. Neither jug has markings. How can you measure exactly 4 gallons of water? | Fill the 5-gallon jug and pour it into the 3-gallon jug, leaving 2 gallons in the 5-gallon jug. Empty the 3-gallon jug, transfer the remaining 2 gallons into it, then fill the 5-gallon jug again and pour from it into the 3-gallon jug until the 3-gallon jug is full. This leaves exactly 4 gallons in the 5-gallon jug. | Fill up the 3-gallon jug | Fill the 5-gallon jug and pour it into the 3-gallon jug, leaving 2 gallons in the 5-gallon jug. Empty the 3-gallon jug, transfer the remaining 2 gallons into it, then fill the 5-gallon jug again and pour from it into the 3-gallon jug until the 3-gallon jug is full. This leaves exactly 4 gallons in the 5-gallon jug. | Fill up the 3-gallon jug |
puzzle_79 | How do you measure exactly 4 liters of water with only a 4-liter, 7-liter, 10-liter, and 3-liter bottle if you are a clever explorer? | You have only a 3-gallon jug and a 5-gallon jug. Neither jug has markings. How can you measure exactly 4 gallons of water? | Fill the 5-gallon jug and pour it into the 3-gallon jug, leaving 2 gallons in the 5-gallon jug. Empty the 3-gallon jug, transfer the remaining 2 gallons into it, then fill the 5-gallon jug again and pour from it into the 3-gallon jug until the 3-gallon jug is full. This leaves exactly 4 gallons in the 5-gallon jug. | Fill up the 4-liter bottle | Fill the 5-gallon jug and pour it into the 3-gallon jug, leaving 2 gallons in the 5-gallon jug. Empty the 3-gallon jug, transfer the remaining 2 gallons into it, then fill the 5-gallon jug again and pour from it into the 3-gallon jug until the 3-gallon jug is full. This leaves exactly 4 gallons in the 5-gallon jug. | Fill up the 4-liter bottle |
ReasoningTrap: Diagnosing Instruction Overriding in Reasoning Models
This repository contains datasets designed to diagnose reasoning rigidity in large language models. These datasets are specially crafted modifications of existing mathematical benchmarks and puzzles to reveal how models override instructions. The paper describing this work can be found here: Reasoning Model is Stubborn: Diagnosing Instruction Overriding in Reasoning Models.
Project Page: https://ReasoningTrap.github.io
The datasets are available on the Hugging Face Hub:
- ConditionedMath (AIME): https://huggingface.co/datasets/ReasoningTrap/AIME
- ConditionedMath (MATH500): https://huggingface.co/datasets/ReasoningTrap/MATH500
- PuzzleTrivial: https://huggingface.co/datasets/ReasoningTrap/PuzzleTrivial
- Downloads last month
- 82