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6305ff0f91
Companion artifact for the paper 'How Far Can an Open Base Model
Self-Improve? Recipes, Limits, and Test-Time Synergy'.
Contents:
- recipe/{train_on_pairs,bootstrap,multi_pair_14b,curriculum_math,eval_raw,eval_plus,confirm}.py
- data/pairs_{7b_40,14b_multi_new60,math_13}.jsonl (released mined pairs)
- controls/mbpp_corrupt_control.py (the +0 negative control)
- docs/{scaling_chart,fig1_headline,fig6_boundary}.png
- REPRODUCE.md (paper claim -> exact command mapping)
13 lines
6.4 KiB
JSON
13 lines
6.4 KiB
JSON
{"problem": "A family went out for dinner and had 3 adults and 2 children. The cost of dinner was $150. How much did each person need to pay?", "solution": "To solve this problem, we need to divide the total cost of dinner by the total number of people. Let's break it down step by step:\n\n1. Calculate the total number of people: 3 adults + 2 children = 5 people.\n2. Divide the total cost of dinner by the total number of people: $150 \u00f7 5 people = $30 per person.\n\nSo, each person needs to pay $30.#### 30", "answer": 30.0}
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{"problem": "The sum of three consecutive integers is 30. One of the integers is 10. What is the sum of the other two integers?", "solution": "1. Let the first integer be x.\n2. The second integer is x + 1.\n3. The third integer is x + 2.\n4. The sum of these three integers is x + (x + 1) + (x + 2) = 3x + 3.\n5. Given that the sum is 30, we have 3x + 3 = 30.\n6. Subtract 3 from both sides to get 3x = 27.\n7. Divide by 3 to find x = 9.\n8. Therefore, the integers are 9, 10, and 11.\n9. The sum of the other two integers (10 and 11) is 10 + 11 = 21.\n#### 21", "answer": 21.0}
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{"problem": "A baker has 25 cookies and wants to pack them into boxes. If each box can hold 5 cookies, and the baker wants to leave a box with fewer than 5 cookies as a gift, how many boxes does the baker need to pack all the remaining cookies?", "solution": "To solve this problem, we need to determine how many boxes are required to pack all the cookies while leaving one box with fewer than 5 cookies as a gift.\n\nStep 1: Calculate the number of boxes needed to pack all the cookies, excluding the gift box.\n- The baker has 25 cookies and each box can hold 5 cookies.\n- Divide the total number of cookies by the number of cookies per box: 25 \u00f7 5 = 5 boxes.\n- Since we want to leave one box as a gift, we will need 5 + 1 = 6 boxes in total.\n\nThe baker needs 6 boxes to pack all the remaining cookies and leave one box with fewer than 5 cookies as a gift.\n\n#### 6", "answer": 6.0}
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{"problem": "Marnie has a box of 18 crayons. She decided to give 5 crayons to her friend. She then decided to buy 3 more crayons. She also decided to give 2 crayons to her teacher. How many crayons does she have left?", "solution": "1. Marnie starts with 18 crayons.\n2. She gives away 5 crayons: 18 - 5 = 13 crayons left.\n3. She buys 3 more crayons: 13 + 3 = 16 crayons.\n4. She gives 2 crayons to her teacher: 16 - 2 = 14 crayons left.\n\n#### 14", "answer": 14.0}
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{"problem": "Jill has a garden. Jill's garden is 18 feet wide. Jill's garden is 15 feet long. How many feet of fencing does jill need to fence her garden?", "solution": "Jill's garden is a rectangle. The perimeter of a rectangle is given by the formula P = 2L + 2W. #### 66", "answer": 66.0}
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{"problem": "I have 3 boxes. One of them is filled with apples. One of them is filled with oranges. One of them is filled with bananas. I know that there are exactly 6 fruits. 2 boxes are empty. How many fruits are in each box?", "solution": "There are 1 apples, 1 oranges, and 4 bananas.#### 1#### 1#### 4", "answer": 1.0}
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{"problem": "The school is having a yard sale. The teachers want to sell 50 old textbooks. If they sell them for $2 each, how much money can they expect to make if they decide to donate 20% of their earnings to a local charity?", "solution": "#### 80\n\nThe teachers can expect to make $80 if they decide to donate 20% of their earnings to a local charity.", "answer": 80.0}
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{"problem": "There are 10 apples in a bag. You take away 3 apples. You then add 5 more apples. How many apples do you have now?", "solution": "1. Start with 10 apples.\n2. Take away 3 apples: 10 - 3 = 7 apples.\n3. Add 5 more apples: 7 + 5 = 12 apples.\n#### 12", "answer": 12.0}
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{"problem": "A pizza has 8 slices. If a family eats 3 slices and then receives an additional 2 slices as a gift, how many slices are left?", "solution": "Let's break down the problem step by step:\n\n1. The pizza starts with 8 slices.\n2. The family eats 3 slices, so there are now 8 - 3 = 5 slices remaining.\n3. The family receives an additional 2 slices as a gift, so there are now 5 + 2 = 7 slices remaining.\n\n#### 7", "answer": 7.0}
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{"problem": "A bird watcher saw 17 birds on Monday, 25 birds on Tuesday, and 18 birds on Wednesday. How many birds did the bird watcher see in total over these three days?", "solution": "Let's break down the problem step by step:\n\n1. **Sum the number of birds seen each day:**\n - Monday: 17 birds\n - Tuesday: 25 birds\n - Wednesday: 18 birds\n\n2. **Add the numbers together:**\n \\[\n 17 + 25 + 18\n \\]\n\n3. **Perform the addition:**\n - First, add the birds seen on Monday and Tuesday:\n \\[\n 17 + 25 = 42\n \\]\n - Next, add the birds seen on Wednesday to the result:\n \\[\n 42 + 18 = 60\n \\]\n\nTherefore, the total number of birds seen over the three days is:\n\\[\n\\boxed{60}\n\\]", "answer": 60.0}
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{"problem": "A baker has 48 cupcakes. She wants to put an equal number of cupcakes in 6 boxes. How many cupcakes will go in each box? Then, she wants to put 25% more cupcakes into each box. How many cupcakes will go in each box now?", "solution": "The baker initially puts 48 cupcakes in 6 boxes, so each box will have 48/6 = 8 cupcakes. Then, she wants to put 25% more cupcakes in each box. The number of additional cupcakes in each box is 8 * 25/100 = 2 cupcakes. Therefore, each box will have a total of 8 + 2 = 10 cupcakes. #### 10", "answer": 10.0}
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{"problem": "A group of 2 friends want to buy a pizza. Each pizza costs $7. How much do they need to spend altogether for 2 pizzas? After eating half of the pizza, how much money will each friend spend?", "solution": "To solve this problem, we will follow these steps:\n\n1. Calculate the total cost of 2 pizzas.\n2. Calculate the cost of half a pizza.\n3. Determine the amount each friend needs to spend.\n\nStep 1: Calculate the total cost of 2 pizzas.\nThe cost of one pizza is $7. Therefore, the cost of 2 pizzas is:\n\\( 2 \\times 7 = 14 \\)\n\nStep 2: Calculate the cost of half a pizza.\nHalf of a pizza is \\( \\frac{2}{2} = 1 \\) pizza. So, the cost of half a pizza is:\n\\( 7 \\times 1 = 7 \\)\n\nStep 3: Determine the amount each friend needs to spend.\nEach friend needs to spend the cost of half a pizza, which is $7.\n\nSo, each friend will spend $7.\n\n#### 7", "answer": 7.0}
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{"problem": "Find the sum of 2, 3, and 4, then divide the result by 2.", "solution": "Step 1: Add 2, 3, and 4.\n(2 + 3 + 4) = 9.\n\nStep 2: Divide the result by 2.\n9 \u00f7 2 = 4.5.\n\n#### 4.5", "answer": 4.5}
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