text: # Hardest math question in the world?
  
  she sold for exactly \$100. She sold
  
  caviar sandwiches for \$5.00 each, the
  
  bologna sandwiches for \$2.00, and
  
  the liverwurst sandwiches for 10 cents.
  
  How many of each type of sandwich
  
  did she make?
  
  Tricky.
  
  C = # of caviar
  
  B = # bologna
  
  L = # of liverwurst
  
  C + B + L = 100
  
  5C + 2B + L/10 = 100
  
  multiply the 2nd equation by 10 and subtract the two
  
  49C + 19B = 900
  
  Now, there are lots of ways to do that, but you need both C and B to be integers. Notice that 900 is divisible by 10. Divide the whole equation by 10
  
  \$4.9 C + \$1.9 B = \$90
  
  Now, we know she need to make exactly \$90 selling just caviar and bologna. Each time she sells a sandwich, she'll have to give a dime in change. To get back to an exact dollar figure, she'll need to sell some multiple of 10 sandwiches. So, make the substitution
  
  C + B = 10 n
  
  Now, solve for C and substitute
  
  49 n - 3 B = 90
  
  Remembering that n and B are both integers, n must be a multiple of 3 (divide that equation by 3 and see). So try, n=3, 6, 9, etc.
  
  For n=3, B = 19
  
  For n=6, B = 68
  
  For n=9, B = 117 (which is impossible.)
  
  If B = 19, then C = 11 and L = 70.
  
  If B = 68, then C = -8 which is impossible.
  
  So, the only possible answer is 11 caviar sandwiches, 19 bologna sandwiches and 70 Liverwurst sandwiches.
  
  #1
  
  ...What are you, a 1st grader?
  
  #2
  
  This is impossible to answer because there can be an infinite number of solutions to this problem.
  
  18 Caviar Sandiwiches = \$90
  
  4 Bologna Sandwiches = \$8
  
  20 Liverwurst Sandwiches = \$2
  
  This all equals \$100. There can be many more solutions to this problem but this is one of them.
  
  #3
  
  You example only equals to 42 sandwiches... might want to check the question again.
  
  #4
explanation: The document contains a math question and multiple answers to this question. The question asks how many of each type of sandwich (caviar, bologna, and liverwurst) were sold to make exactly \$100, given the prices of each type of sandwich. The document also includes several responses with different solutions and explanations.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Hardest math question in the world?
  
  she sold for exactly \$100. She sold
  
  caviar sandwiches for \$5.00 each, the
  
  bologna sandwiches for \$2.00, and
  
  the liverwurst sandwiches for 10 cents.
  
  How many of each type of sandwich
  
  did she make?
  
  Tricky.
  
  C = # of caviar
  
  B = # bologna
  
  L = # of liverwurst
  
  C + B + L = 100
  
  5C + 2B + L/10 = 100
  
  multiply the 2nd equation by 10 and subtract the two
  
  49C + 19B = 900
  
  Now, there are lots of ways to do that, but you need both C and B to be integers. Notice that 900 is divisible by 10. Divide the whole equation by 10
  
  \$4.9 C + \$1.9 B = \$90
  
  Now, we know she need to make exactly \$90 selling just caviar and bologna. Each time she sells a sandwich, she'll have to give a dime in change. To get back to an exact dollar figure, she'll need to sell some multiple of 10 sandwiches. So, make the substitution
  
  C + B = 10 n
  
  Now, solve for C and substitute
  
  49 n - 3 B = 90
  
  Remembering that n and B are both integers, n must be a multiple of 3 (divide that equation by 3 and see). So try, n=3, 6, 9, etc.
  
  For n=3, B = 19
  
  For n=6, B = 68
  
  For n=9, B = 117 (which is impossible.)
  
  If B = 19, then C = 11 and L = 70.
  
  If B = 68, then C = -8 which is impossible.
  
  So, the only possible answer is 11 caviar sandwiches, 19 bologna sandwiches and 70 Liverwurst sandwiches.
  
  #1
  
  ...What are you, a 1st grader?
  
  #2
  
  This is impossible to answer because there can be an infinite number of solutions to this problem.
  
  18 Caviar Sandiwiches = \$90
  
  4 Bologna Sandwiches = \$8
  
  20 Liverwurst Sandwiches = \$2
  
  This all equals \$100. There can be many more solutions to this problem but this is one of them.
  
  #3
  
  You example only equals to 42 sandwiches... might want to check the question again.
  
  #4
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and multiple answers to this question. The question asks how many of each type of sandwich (caviar, bologna, and liverwurst) were sold to make exactly \$100, given the prices of each type of sandwich. The document also includes several responses with different solutions and explanations.
  
  Label: multiple-question-and-answer