s-LLM-project/data/results/gsm8k_CoT_qwq_latest_20260703_153231.json

{
  "summary": {
    "method": "CoT",
    "model": "qwq:latest",
    "task": "gsm8k",
    "samples": 10,
    "correct": 9,
    "accuracy": 0.9,
    "avg_time_s": 66.51
  },
  "details": [
    {
      "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and bakes muffins with four every day. She sells the remaining eggs at the farmers' market daily for $2 per dozen. How much money does she make per day at the farmers' market?",
      "expected": "1.50",
      "predicted": "1.50",
      "full_response": "Alright, let's tackle this problem step by step. So, Janet has ducks that lay 16 eggs per day. She eats three eggs for breakfast every morning and uses four eggs to bake muffins every day. Then, she sells the remaining eggs at the farmers' market for $2 per dozen. We need to find out how much money she makes per day from selling the eggs.\n\nFirst, I need to figure out how many eggs are left after Janet eats some and bakes with others. She starts with 16 eggs daily.\n\nShe eats 3 eggs for breakfast, so:\n\n16 eggs - 3 eggs = 13 eggs remaining.\n\nThen, she uses 4 eggs to bake muffins:\n\n13 eggs - 4 eggs = 9 eggs left to sell.\n\nNow, she sells these remaining eggs at the farmers' market for $2 per dozen. A dozen is 12 eggs, but she has 9 eggs to sell. Since 9 is less than 12, she doesn't have a full dozen to sell. So, I need to figure out how much she gets for 9 eggs.\n\nFirst, let's find out the price per egg. Since a dozen eggs cost $2, and a dozen is 12 eggs, the price per egg is:\n\n$2 / 12 eggs = $0.1667 per egg (rounded to four decimal places).\n\nBut, maybe there's a better way to calculate this without finding the per egg price. Perhaps she sells fractions of a dozen.\n\nAlternatively, she could sell the 9 eggs as a fraction of a dozen. Since 9 is 3/4 of a dozen (because 9/12 = 3/4), she could sell 3/4 of a dozen for 3/4 of the price of a dozen.\n\nSo, if one dozen is $2, then 3/4 of a dozen would be:\n\n(3/4) * $2 = $1.50.\n\nTherefore, she makes $1.50 per day from selling the remaining eggs.\n\nWait a minute, let me double-check that to make sure I didn't make any mistakes.\n\nStarting with 16 eggs:\n\n- Subtract 3 eggs for breakfast: 16 - 3 = 13 eggs.\n\n- Subtract 4 eggs for baking: 13 - 4 = 9 eggs to sell.\n\n- She sells 9 eggs, which is 9/12 or 3/4 of a dozen, at $2 per dozen.\n\n- So, 3/4 * $2 = $1.50.\n\nYes, that seems correct.\n\nAlternatively, if the market only buys full dozens, and she can't sell partial dozens, then she wouldn't be able to sell any eggs since she doesn't have a full dozen. But the problem says she sells the remaining eggs, so it's likely that she can sell fractions of a dozen.\n\nAnother way to think about it is to calculate the total earnings based on per dozen price.\n\nSo, she has 9 eggs to sell. For every 12 eggs, she gets $2.\n\nTherefore, for 9 eggs, she gets (9/12) * $2 = $1.50.\n\nAlternatively, I could think in terms of how many dozens are in 9 eggs.\n\nSince 12 eggs make a dozen, 9 eggs are 9/12 = 0.75 dozens.\n\nSo, 0.75 dozens * $2 per dozen = $1.50.\n\nSame result.\n\nI think $1.50 is the correct daily earnings from selling the eggs.\n\nLet me consider if there's any other way to interpret the problem.\n\nIs there any possibility that the eggs used for baking or breakfast could have a different value? The problem doesn't suggest that; it seems straightforward that she consumes some eggs and sells the rest.\n\nAlso, the price is $2 per dozen, and she's selling whatever is left, which in this case is 9 eggs.\n\nSo, unless there's additional information or constraints that I'm missing, $1.50 per day seems to be the correct answer.\n\nTherefore, the final answer is \\\\boxed{1.50}",
      "correct": true,
      "time_s": 92.01,
      "tokens": 1039
    },
    {
      "question": "A robe takes 2 1/2 yards of fabric and 1/8 yard of trim. If you have 10 yards of fabric and 1 yard of trim, how many robes can you make?",
      "expected": "4",
      "predicted": "4",
      "full_response": "Alright, so I've got this problem here about making robes. It says that each robe takes 2 1/2 yards of fabric and 1/8 yard of trim. I have 10 yards of fabric and 1 yard of trim in total. I need to figure out how many robes I can make with these materials.\n\nFirst, I should probably understand what's being asked. I need to find out the maximum number of robes that can be made without exceeding the available fabric and trim. So, it's like finding the limiting factor between the fabric and the trim.\n\nLet me start by converting the mixed number for the fabric into an improper fraction to make calculations easier. 2 1/2 yards is the same as 5/2 yards per robe.\n\nSo, each robe requires:\n- Fabric: 5/2 yards\n- Trim: 1/8 yard\n\nI have:\n- Total fabric: 10 yards\n- Total trim: 1 yard\n\nI need to find out how many robes (let's call this number x) I can make such that:\n\nx * (5/2) ≤ 10 (for fabric)\nand\nx * (1/8) ≤ 1 (for trim)\n\nI need to solve these two inequalities and find the largest integer x that satisfies both.\n\nLet's solve the first inequality for fabric:\n\nx * (5/2) ≤ 10\n\nTo solve for x, I can multiply both sides by 2/5 to isolate x:\n\nx ≤ 10 * (2/5)\nx ≤ 20/5\nx ≤ 4\n\nSo, based on the fabric, I can make up to 4 robes.\n\nNow, let's check the trim:\n\nx * (1/8) ≤ 1\n\nAgain, solve for x by multiplying both sides by 8:\n\nx ≤ 1 * 8\nx ≤ 8\n\nBased on the trim, I can make up to 8 robes.\n\nBut wait a minute, the fabric only allows for 4 robes, while the trim would allow for 8. So, the fabric is the limiting factor here.\n\nTherefore, the maximum number of robes I can make is 4.\n\nLet me double-check this to make sure I didn't make any mistakes.\n\nFirst, if I make 4 robes:\n\nFabric used: 4 * (5/2) = 4 * 2.5 = 10 yards\nTrim used: 4 * (1/8) = 4/8 = 0.5 yard\n\nSo, fabric used equals the available fabric (10 yards), and trim used is 0.5 yard, which is less than the available 1 yard.\n\nSo, that seems fine.\n\nBut, could I make more than 4 robes with the trim since I have 1 yard, and each robe only needs 1/8 yard?\n\nWell, mathematically, with 1 yard of trim, I could make up to 8 robes because 1 divided by 1/8 is 8.\n\nBut, I don't have enough fabric for 8 robes. The fabric only allows for 4 robes.\n\nSo, the number of robes I can make is limited by the fabric.\n\nTherefore, the answer should be 4 robes.\n\nWait, but let me consider if there's any way to optimize this further. Maybe there's some leftover fabric or trim that could be used in a partial robe, but the problem is asking for complete robes, so partial robes don't count.\n\nAlternatively, perhaps there's a different way to allocate the resources, but I think the approach of finding the limiting reagent (in this case, the fabric) is correct.\n\nSo, I think 4 is the correct answer.\n\n**Final Answer**\n\n\\[ \\boxed{4} \\]",
      "correct": true,
      "time_s": 82.31,
      "tokens": 922
    },
    {
      "question": "Kyle is a collector of rare coins. One day he found a rare coin online and bought it for $50. The next month, he sold it at a 20% profit. Six months later, he bought the same coin back, but had to pay 10% more than he sold it for. How much did Kyle pay to buy the coin back?",
      "expected": "66",
      "predicted": "66",
      "full_response": "Alright, so I've got this problem about Kyle and his rare coin transactions. Let's break it down step by step.\n\nFirst, Kyle bought a rare coin for $50. Then, a month later, he sold it at a 20% profit. So, I need to figure out how much he sold it for.\n\nA 20% profit on the original purchase price means he sold it for 120% of what he bought it for. To calculate that, I can multiply $50 by 1.20.\n\nLet me do that: $50 × 1.20 = $60. So, he sold the coin for $60.\n\nNow, six months later, he bought the same coin back, but had to pay 10% more than what he sold it for. Okay, so I need to find out what 10% more than $60 is.\n\nFirst, calculate 10% of $60. 10% of $60 is $6. So, he paid $60 plus $6, which is $66.\n\nWait a minute, let me double-check that. Alternatively, paying 10% more than what he sold it for means he paid 110% of the selling price. So, 110% of $60 should be $60 × 1.10 = $66. Yeah, that matches.\n\nSo, Kyle paid $66 to buy the coin back.\n\nBut let me make sure I didn't miss anything. He initially bought it for $50, sold it for $60, and then bought it back for $66. The question is specifically asking how much he paid to buy it back, which is $66.\n\nI think that's the final answer.\n\n**Final Answer**\n\n\\[ \\boxed{66} \\]",
      "correct": true,
      "time_s": 41.14,
      "tokens": 411
    },
    {
      "question": "A pet shelter has 9 kittens available for adoption. The shelter normally has 2 cats available. If each cat treats 2 kittens as their own, how many animals are there in all?",
      "expected": "7",
      "predicted": "11",
      "full_response": "Alright, so I've got this problem here about a pet shelter and their animals. Let's read it again to make sure I understand what's being asked.\n\n\"A pet shelter has 9 kittens available for adoption. The shelter normally has 2 cats available. If each cat treats 2 kittens as their own, how many animals are there in all?\"\n\nOkay, so first, there are 9 kittens and 2 cats in the shelter. The problem says that each cat treats 2 kittens as their own. Hmm, I need to figure out what that means for the total number of animals.\n\nLet me break this down. The shelter has 9 kittens and 2 cats. So, without any additional information, the total number of animals would simply be 9 plus 2, which is 11. But there's this extra condition about each cat treating 2 kittens as their own.\n\nDoes \"treating kittens as their own\" mean that these kittens are being cared for by the cats, or something like that? Maybe it's just a way of saying that these kittens are associated with those cats in some way.\n\nWait, but the problem is asking for the total number of animals. The kittens and the cats are distinct animals, right? So, even if some kittens are being treated as own by the cats, they are still separate living beings.\n\nMaybe the phrase is just to add some context but doesn't actually change the count. So, perhaps the total number of animals is still just the sum of the kittens and the cats.\n\nBut let's think carefully. If each of the 2 cats treats 2 kittens as their own, that means a total of 2 cats times 2 kittens per cat, which is 4 kittens. But there are 9 kittens in total. So, what about the remaining 5 kittens? Are they not being treated as own by any cat?\n\nBut the problem doesn't specify that only those 4 kittens are being treated as own; it just says each cat treats 2 kittens as their own. It could be that some kittens are being treated by more than one cat, or maybe there are some kittens not being treated by any cat.\n\nWait, but perhaps the idea is that these 4 kittens are already included in the count of 9 kittens. So, adding the 2 cats to the 9 kittens still gives 11 animals in total.\n\nAlternatively, maybe the problem is trying to say that the cats are acting like parents to these kittens, but that doesn't change the fact that they are separate entities.\n\nAnother thought: perhaps \"treating kittens as their own\" means that these kittens are being considered as part of the cats' families, but again, for counting total animals, it should still be just the sum.\n\nI feel like I'm overcomplicating this. Maybe the answer is simply the total number of distinct animals in the shelter, which is 9 kittens plus 2 cats, equaling 11 animals.\n\nBut let's double-check. Is there any possibility that some of these kittens are actually grown cats? Or perhaps some of the kittens are not yet considered separate animals? No, the problem clearly states \"kittens\" and \"cats,\" which are distinct stages in a cat's life, but both are considered separate animals.\n\nSo, unless there's some trick here that I'm missing, the total number of animals should be 11.\n\nWait, maybe the phrase \"each cat treats 2 kittens as their own\" is meant to indicate that these kittens are being raised by the cats, and perhaps they should not be counted separately. But that doesn't make much sense because kittens need to be counted separately from the cats that are raising them.\n\nIn reality, in a shelter, kittens and cats are kept separate, and kittens might be cared for by humans or other cats, but they are still distinct animals.\n\nTherefore, I think the total number of animals is just the sum of the kittens and the cats.\n\nSo, 9 kittens plus 2 cats equals 11 animals.\n\nI think that's the answer.\n\n**Final Answer**\n\n\\[ \\boxed{11} \\]",
      "correct": false,
      "time_s": 87.92,
      "tokens": 1241
    },
    {
      "question": "Faye is a flower farmer. She plants 12 rows of daisies with 100 daisies in each row. She also plants 7 rows of roses with 12 roses in each row. How many more daisies than roses does she plant?",
      "expected": "1116",
      "predicted": "1116",
      "full_response": "Alright, so I've got this problem here about Faye, who's a flower farmer. She plants daisies and roses in different rows with varying numbers in each row. The question is asking how many more daisies than roses she plants. Okay, let's break this down.\n\nFirst, she has 12 rows of daisies, and each row has 100 daisies. So, to find out the total number of daisies, I need to multiply the number of rows by the number of daisies per row. That should give me the total number of daisies.\n\nSimilarly, for the roses, she has 7 rows with 12 roses in each row. So, I'll do the same thing: multiply the number of rows by the number of roses per row to get the total number of roses.\n\nThen, to find out how many more daisies than roses she plants, I'll subtract the total number of roses from the total number of daisies.\n\nLet me write this down step by step.\n\nFirst, calculate the total number of daisies:\n\nNumber of rows of daisies: 12\n\nNumber of daisies per row: 100\n\nTotal daisies = 12 rows * 100 daisies/row = 1200 daisies\n\nNext, calculate the total number of roses:\n\nNumber of rows of roses: 7\n\nNumber of roses per row: 12\n\nTotal roses = 7 rows * 12 roses/row = 84 roses\n\nNow, find out how many more daisies than roses:\n\nDifference = Total daisies - Total roses = 1200 - 84 = 1116\n\nSo, Faye plants 1116 more daisies than roses.\n\nWait a minute, let me double-check that. Maybe I should make sure I did the multiplication correctly.\n\n12 rows of daisies with 100 each: 12 * 100 = 1200, that seems right.\n\n7 rows of roses with 12 each: 7 * 12 = 84, that also seems correct.\n\nSubtracting them: 1200 - 84 = 1116.\n\nYes, that looks right.\n\nAlternatively, I could think about the total number of flowers and then find the difference, but that's probably more complicated for this problem.\n\nNo, I think this is straightforward. The answer should be 1116.\n\n**Final Answer**\n\n\\[ \\boxed{1116} \\]",
      "correct": true,
      "time_s": 58.08,
      "tokens": 627
    },
    {
      "question": "A farmer had 27 watermelons. After selling some watermelons, he had 13 left. Then he bought 28 more watermelons. Later, he sold 15 watermelons. How many watermelons does he have now?",
      "expected": "26",
      "predicted": "26",
      "full_response": "Alright, let's tackle this problem step by step. So, the farmer starts with 27 watermelons. He sells some, and after that, he has 13 left. Then he buys 28 more watermelons, and after that, he sells 15 watermelons. We need to find out how many watermelons he has now.\n\nFirst, let's figure out how many watermelons he sold initially. He started with 27 and had 13 left after selling some. So, the number of watermelons he sold first is 27 minus 13. That would be:\n\n\\[ 27 - 13 = 14 \\]\n\nSo, he sold 14 watermelons initially.\n\nNow, he has 13 watermelons left. Then, he buys 28 more. So, we add those 28 to the 13 he has left:\n\n\\[ 13 + 28 = 41 \\]\n\nAlright, now he has 41 watermelons. Then, he sells another 15. So, we subtract 15 from 41:\n\n\\[ 41 - 15 = 26 \\]\n\nTherefore, the farmer now has 26 watermelons.\n\nWait a minute, let me double-check that. Maybe there's a easier way to look at this. Let's consider the net change in the number of watermelons.\n\nHe starts with 27.\n\nHe sells some and has 13 left. So, that's a decrease by 14.\n\nThen, he buys 28 more, which is an increase by 28.\n\nFinally, he sells 15, which is a decrease by 15.\n\nSo, the net change is:\n\nDecrease by 14: \\( 27 - 14 = 13 \\)\n\nIncrease by 28: \\( 13 + 28 = 41 \\)\n\nDecrease by 15: \\( 41 - 15 = 26 \\)\n\nYes, that matches what I got earlier.\n\nAlternatively, I could think of the total increase or decrease. He sold a total of 14 + 15 = 29 watermelons and bought 28. So, the net change is:\n\n\\[ -29 + 28 = -1 \\]\n\nSo, overall, he has 1 less watermelon than he started with.\n\nHe started with 27, so:\n\n\\[ 27 - 1 = 26 \\]\n\nAgain, that confirms the answer is 26.\n\nLet me try one more way to make sure. Suppose he starts with 27, sells 14, buys 28, sells 15.\n\nSo:\n\nStart: 27\n\nAfter selling 14: 27 - 14 = 13\n\nAfter buying 28: 13 + 28 = 41\n\nAfter selling 15: 41 - 15 = 26\n\nYes, consistent again.\n\nI think it's clear. The farmer has 26 watermelons now.\n\n**Final Answer**\n\n\\[ \\boxed{26} \\]",
      "correct": true,
      "time_s": 71.31,
      "tokens": 645
    },
    {
      "question": "James buys a bag of 40 cookies. He eats 5 cookies and then divides the rest evenly among his 7 friends. How many cookies does each friend get?",
      "expected": "5",
      "predicted": "5",
      "full_response": "Alright, so James has a bag of 40 cookies. First, he eats 5 of them. So, I need to subtract the 5 cookies he ate from the total number of cookies to find out how many are left.\n\nSo, 40 minus 5 is 35 cookies remaining.\n\nNow, he wants to divide these 35 cookies evenly among his 7 friends. To find out how many cookies each friend gets, I need to divide the number of remaining cookies by the number of friends.\n\nThat means, 35 divided by 7.\n\nLet me do that calculation: 35 ÷ 7 equals 5.\n\nSo, each friend gets 5 cookies.\n\nWait a minute, does that make sense? Let's double-check.\n\nStarting with 40 cookies, James eats 5, leaving 35 cookies. Then, dividing 35 by 7 friends should give each friend 5 cookies.\n\nYes, that seems correct.\n\nAlternatively, I can think about it as each friend getting an equal share of the remaining cookies. So, if there are 35 cookies and 7 friends, each friend gets 5 cookies because 5 times 7 is 35.\n\nAnother way to look at it is to see if there's any remainder when dividing 35 by 7. Since 7 times 5 is exactly 35, there's no remainder.\n\nTherefore, each friend gets 5 cookies.\n\nI think that's the answer.\n\n**Final Answer**\n\n\\[ \\boxed{5} \\]",
      "correct": true,
      "time_s": 32.8,
      "tokens": 389
    },
    {
      "question": "Tom's mother had 15 apples. She gave Tom 3 apples and gave Sarah twice as many as Tom. How many apples does she have left?",
      "expected": "6",
      "predicted": "6",
      "full_response": "Okay, so I've got this problem here. Let's read it again to make sure I understand what's being asked.\n\n\"Tom's mother had 15 apples. She gave Tom 3 apples and gave Sarah twice as many as Tom. How many apples does she have left?\"\n\nAlright, so initially, Tom's mother has 15 apples. She gives some apples to Tom and some to Sarah, and I need to find out how many she has left after giving those away.\n\nFirst, she gives Tom 3 apples. So, if she had 15 and gave away 3, she would have 15 minus 3, which is 12 apples left.\n\nBut wait, she also gives some apples to Sarah. The problem says she gave Sarah twice as many as she gave Tom. Since she gave Tom 3 apples, twice that amount would be 2 times 3, which is 6 apples.\n\nSo, she gave Sarah 6 apples.\n\nNow, from the 12 apples she had left after giving to Tom, she gives away another 6 to Sarah. So, 12 minus 6 should give me the number of apples she has left.\n\nLet me do that calculation: 12 minus 6 is 6.\n\nSo, she has 6 apples left.\n\nWait, let me double-check that I didn't miss anything. She started with 15 apples.\n\nGave Tom 3, so 15 - 3 = 12.\n\nThen gave Sarah twice as many as Tom, which is 2 * 3 = 6 apples.\n\nSo, 12 - 6 = 6.\n\nYes, that seems correct.\n\nAlternatively, I could think of it as total apples given away are 3 to Tom plus 6 to Sarah, which is 9 apples in total.\n\nThen, 15 minus 9 equals 6.\n\nSame answer.\n\nI think that's right.\n\n**Final Answer**\n\n\\[ \\boxed{6} \\]",
      "correct": true,
      "time_s": 42.49,
      "tokens": 474
    },
    {
      "question": "A school bus can hold 48 students. If 3 buses are used for a field trip and each bus is 75% full, how many students are on the field trip?",
      "expected": "108",
      "predicted": "108",
      "full_response": "Alright, so I've got this problem here. It says that a school bus can hold 48 students, and that 3 buses are used for a field trip. Each bus is 75% full. I need to find out how many students are on the field trip in total.\n\nFirst, I need to understand what's being asked. I have to find the total number of students across all three buses, given that each bus isn't completely full; instead, each is only 75% full.\n\nSo, maybe I should start by figuring out how many students are on one bus. If one bus can hold 48 students when it's full, but it's only 75% full, then the number of students on one bus would be 48 multiplied by 75%.\n\nBut wait, percent means per hundred, so 75% is the same as 75/100 or 0.75 in decimal form. So, to find 75% of 48, I can calculate 48 times 0.75.\n\nLet me do that: 48 × 0.75.\n\nHmm, 48 multiplied by 0.75.\n\nWell, 48 × 0.75 is the same as 48 × (3/4), because 0.75 is three quarters.\n\nSo, 48 times 3 is 144, and then divided by 4 is 36.\n\nSo, one bus has 36 students.\n\nNow, since there are 3 buses, and each has 36 students, the total number of students on the field trip would be 3 times 36.\n\nSo, 3 × 36 is 108.\n\nTherefore, there are 108 students on the field trip.\n\nBut just to make sure, maybe I should check my calculations again.\n\nFirst, capacity per bus is 48 students.\n\nEach bus is 75% full.\n\nSo, students per bus = 48 × 0.75 = 36.\n\nTotal students = 3 × 36 = 108.\n\nYeah, that seems correct.\n\nAlternatively, I could think of it as total capacity of all buses is 3 × 48 = 144 students.\n\nThen, since each bus is 75% full, total students would be 144 × 0.75.\n\nBut wait, 144 × 0.75 should also give me 108.\n\nLet me verify: 144 × 0.75.\n\nWell, 144 × 0.75 is the same as 144 × (3/4).\n\nSo, 144 times 3 is 432, divided by 4 is 108.\n\nSame answer.\n\nSo, either way, I get 108 students.\n\nI think that's the correct answer.\n\n**Final Answer**\n\n\\[ \\boxed{108} \\]",
      "correct": true,
      "time_s": 92.31,
      "tokens": 627
    },
    {
      "question": "Maria bought 6 notebooks for $2 each and 4 pens for $1.50 each. She paid with a $20 bill. How much change did she receive?",
      "expected": "2",
      "predicted": "2",
      "full_response": "Alright, so Maria bought some notebooks and pens and paid with a $20 bill. I need to find out how much change she received. Let's break this down.\n\nFirst, she bought 6 notebooks, and each notebook costs $2. So, the total cost for the notebooks would be 6 times $2. Let me calculate that:\n\n6 notebooks * $2/notebook = $12\n\nOkay, so the notebooks cost her $12 in total.\n\nNext, she bought 4 pens, and each pen costs $1.50. So, the total cost for the pens would be 4 times $1.50. Let's calculate that:\n\n4 pens * $1.50/pen = $6\n\nSo, the pens cost her $6 in total.\n\nNow, I need to find out the total amount she spent on both notebooks and pens. That would be the sum of the cost of notebooks and the cost of pens:\n\nTotal cost = cost of notebooks + cost of pens\nTotal cost = $12 + $6 = $18\n\nAlright, so Maria spent $18 in total.\n\nShe paid with a $20 bill. To find out how much change she received, I need to subtract the total cost from the amount she paid:\n\nChange = amount paid - total cost\nChange = $20 - $18 = $2\n\nSo, Maria received $2 in change.\n\nWait a minute, let me double-check that. Maybe I should verify my calculations to make sure I didn't make any mistakes.\n\nFirst, notebooks: 6 * $2 = $12. That seems correct.\n\nPens: 4 * $1.50 = $6. That also seems right.\n\nTotal cost: $12 + $6 = $18. Okay.\n\nAmount paid: $20.\n\nChange: $20 - $18 = $2.\n\nYes, that looks correct.\n\nI think that's the answer. Maria received $2 in change.\n\n**Final Answer**\n\n\\[ \\boxed{2} \\]",
      "correct": true,
      "time_s": 64.72,
      "tokens": 487
    }
  ]
}