Datasets:
data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
t01_math | [
{
"role": "user",
"content": "The original price of an item is $\\$11$. The new price is $\\$13$. How many dollars is Tom going to save on this purchase?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::a35d21cfd3a5bbd8065b6e2e",
"index": "kd::a35d21cfd3a5bbd8065b6e2e",
"lang": "en",
"rubrics": [
{
"criterion": "Identify whether the new price is higher or lower than the original price to determine if savings exist.",
"points": 2,
"tags": {
"judge": false,
"in... |
t01_math | [
{
"role": "user",
"content": "A l Heaven, theKatians can getCF (CometFish) Internet access to play viceCO consisted of $2x$ dollars, becoming you add $M$ dollars extra for private Macabout constructed giant machines that.util the lawsometry machine, taking classic \"gigawattdoesit\");\n\nthe;i\r\nYou are a ... | math | {
"ground_truth": "2x + M",
"style": "rule"
} | {
"uid": "kd::c0b51766ee7598d7c853d7f2",
"index": "kd::c0b51766ee7598d7c853d7f2",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 100 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Round 7.03 up to the nearest whole number?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"uid": "kd::5b1d742b46103be93fde4609",
"index": "kd::5b1d742b46103be93fde4609",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the digit immediately to the right of the decimal point to determine the rounding direction.",
"points": 2,
"tags": {
"judge": false,
"injec... |
t01_math | [
{
"role": "user",
"content": "변의 길이가 \\( a \\)인 정육면체에서 점 \\( E, F, G, H \\)는 각각 변 \\( AB, A_{1}D_{1}, A_{1}B_{1}, BC \\)의 중점이다. 사면체 \\( EFGH \\)의 외접구 반지름과 내접구 반지름의 비를 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "2 + \\sqrt{6}",
"style": "rule"
} | {
"uid": "kd::df151fda63ef20b7c5123cb0",
"index": "kd::df151fda63ef20b7c5123cb0",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 \\frac{abc}{4V} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "적색 편이 별의 주기는 회전하는 지구의 하루 길이의 $\\frac{360}{445}$배이다. 피터가 180개의 케이크데이 동안 몇 개의 적색 편이 별을 볼 수 있는가?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "222",
"style": "rule"
} | {
"uid": "kd::a59555eb037bb94fac550d16",
"index": "kd::a59555eb037bb94fac550d16",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 222.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Sandy has $30 in her piggy bank. She decides to invest this money in 4 stocks, and her friend Hul has the same amount of money as Sandy's and they join forces with Rob who has twice the amount of money as Sandy and Hul, divided equally among the 4 stocks. What is the amount of... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"uid": "kd::74714923330fd05dd2d489b9",
"index": "kd::74714923330fd05dd2d489b9",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 120 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Determine whether the number of orbits of the natural action of order-preserving bijections of $\\mathbb{Q}$ on $\\mathbb{Q}^n$ is finite. An order-preserving map $f : \\mathbb{Q} \\to \\mathbb{Q}$ satisfies $x > y \\implies f(x) > f(y)$. Let $\\text{Aut}(\\mathbb{Q}) = \\{ f :... | math | {
"ground_truth": "Yes",
"style": "rule"
} | {
"uid": "kd::6a8649d0ec171266f17a5613",
"index": "kd::6a8649d0ec171266f17a5613",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "There are 16 cows or 25 foxes in a country. If all the foxes are kept inside the same barn, and each barn contains 3 foxes inside, how many barns are need to accommodate all the foxes and the cows?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"uid": "kd::48b92d6eddba274535bb998c",
"index": "kd::48b92d6eddba274535bb998c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 8.333 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Give the only solution (x,y) in Z_7.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "(0,0)",
"style": "rule"
} | {
"uid": "kd::999f24d5f746327689d52456",
"index": "kd::999f24d5f746327689d52456",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 16 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "If the total cost of books purchased exceeds $800 by exactly 4 times the cost of $5 notebooks, what is the total cost of the notebook if the books' original total cost was $1000?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::14b1d55fee91b5237ebd38c4",
"index": "kd::14b1d55fee91b5237ebd38c4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 200 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Determine the integer $n,$ $-90 < n < 90,$ for which $\\cos n^\\circ = \\cos 1000^\\circ.$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "80",
"style": "rule"
} | {
"uid": "kd::2844c94e975ff0ada8767e4d",
"index": "kd::2844c94e975ff0ada8767e4d",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 280 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "On a map of Euclid County, $\\frac{1}{3}$ inch represents 2 miles. Lake Pythagoras is represented on the map by a right triangle with sides 1 inch, $\\frac{4}{3}$ inches, and $\\frac{5}{3}$ inches. What is the ratio of the area of the actual Lake Pythagoras to the area of its c... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"uid": "kd::91949b2aab4bfb6e9714c790",
"index": "kd::91949b2aab4bfb6e9714c790",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 25 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "What is the compound interest paid on a sum of Rs. 4500 for the period of 2 years at a certain interest rate per annum if the interest is Rs. 945.0000000000009?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "10\\%",
"style": "rule"
} | {
"uid": "kd::3d11952eb74e1c679fd7ccfb",
"index": "kd::3d11952eb74e1c679fd7ccfb",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 5445 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "변호사 존은 15분당 평균 1명의 고객이 도착하는 포아송 분포에 따라 고객을 받습니다. 금요일 오전 10시부터 오후 12시 사이에 존은 10명의 고객을 받았습니다. 그날(금요일) 오전 9시부터 오후 1시 사이에 존이 받을 것으로 예상되는 고객 수는 얼마입니까?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"uid": "kd::ebc59927083b693997483850",
"index": "kd::ebc59927083b693997483850",
"lang": "ko",
"rubrics": [
{
"criterion": "포아송 과정의 독립 증분 성질을 이용하여 관측된 구간과 관측되지 않은 구간을 분리하여 생각하라.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold_rank": 1,
"s... |
t01_math | [
{
"role": "user",
"content": "At the exhibit, the number of visitors to the hall models the equation 3t^2+5t+12 where t is the number of seconds after door opening and the number of people is in the hundred's place. How many people were in the exhibit; 10 seconds after its opening?\n\nSolve the problem. Sho... | math | {
"ground_truth": "362",
"style": "rule"
} | {
"uid": "kd::01e2b1718dbe0b973cb5da2c",
"index": "kd::01e2b1718dbe0b973cb5da2c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 300 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "I bought a new bike for $2000 and I have money oldest circuit board. It cost $4,000. How much does it cost for the bike total?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "6000",
"style": "rule"
} | {
"uid": "kd::52996b7d1c5acddde32b722f",
"index": "kd::52996b7d1c5acddde32b722f",
"lang": "en",
"rubrics": [
{
"criterion": "Identify all individual costs mentioned in the problem statement to prepare for summation.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "TLP 80 is a pipe that can hold 80 arete pitches. An arete pitch is an arbitrary unit of storage space for sports equipment, usually laundry. If there are 10 80 arete pitch pipes, how many people can it hold who want a place to store, assuming each of them also stores their age... | math | {
"ground_truth": "600",
"style": "rule"
} | {
"uid": "kd::87dd3749710ebb59d6d74660",
"index": "kd::87dd3749710ebb59d6d74660",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 800 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "How do you simplify the expression #7/10 + 1/2# and express it as #6/(5x)#?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"uid": "kd::cba8b8077432d8502fdb18b7",
"index": "kd::cba8b8077432d8502fdb18b7",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 30 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "A box and palette of 18 spoons had to be packed into a crate for window dressing. If the same box had been able to hold 30 spoons, how many moreliest ContrastProbe contrast trials would the box have to conduct?\n\nSolve the problem. Show your reasoning, then put the final answe... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"uid": "kd::c37124b7cc85027b358f81f5",
"index": "kd::c37124b7cc85027b358f81f5",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the current capacity and the hypothetical capacity to determine the difference between them.",
"points": 2,
"tags": {
"judge": false,
"injec... |
t01_math | [
{
"role": "user",
"content": "Answer only yes or no: does the property imply continuity at x=1?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "No",
"style": "rule"
} | {
"uid": "kd::cb470298ad3fd5fd1368b97c",
"index": "kd::cb470298ad3fd5fd1368b97c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Tony grew vegetables last summer. When he was planting beans, he bought 9 plots of land with 8 rows of 6 poles each plot. Each pole has 7 seeds that can grow 2 beans for every pole. How many beans can Tony grow per plot?\n\nSolve the problem. Show your reasoning, then put the f... | math | {
"ground_truth": "672",
"style": "rule"
} | {
"uid": "kd::b91e8ca4cc53344d943fb354",
"index": "kd::b91e8ca4cc53344d943fb354",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 48 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "How do I simplify $\\cos(\\sin^{-1} x)$ to get the final answer of $y = \\cos (C)x + \\sin(C)\\sqrt{1-x^2}$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "\\sqrt{1-x^{2}}",
"style": "rule"
} | {
"uid": "kd::162f2c4d1ae032ce8dadde62",
"index": "kd::162f2c4d1ae032ce8dadde62",
"lang": "en",
"rubrics": [
{
"criterion": "Introduce a new angle variable to represent the inverse sine function and rewrite the expression using right triangle definitions.",
"points": 2,
"tags": {
"... |
t01_math | [
{
"role": "user",
"content": "Answer Yes or No: is the sequence Cauchy?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "No",
"style": "rule"
} | {
"uid": "kd::76cd9e5ff06e56453c2b92e8",
"index": "kd::76cd9e5ff06e56453c2b92e8",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{2\\pi} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "James decides to make granola for his mean trips. Its tri Playing in free school Wednesday, he buys a $5 coupon for 100 granola bars ($0.49 each). Tom buys 8 midnight package. How much money will they save the difference after the coupon is used?\n\nSolve the problem. Show your... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::d00f409eb8789ec3971f2020",
"index": "kd::d00f409eb8789ec3971f2020",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 44 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Find the solution to the differential equation $$\\frac{dy}{dx} = \\frac{3x-2}{3y+4}, y(1)=2$$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "y = \\frac{-4+\\sqrt{9x^2-12x+103}}{3}",
"style": "rule"
} | {
"uid": "kd::ba21b40a36a1afa4f93b1e83",
"index": "kd::ba21b40a36a1afa4f93b1e83",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -48 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Using mathematical induction, prove that for all positive integers \\( n \\), the following equation holds: \n\\[ 1 \\cdot 1! + 2 \\cdot 2! + \\cdots + n \\cdot n! = (n + 1)! - 1. \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "1 \\cdot 1! + 2 \\cdot 2! + \\cdots + n \\cdot n! = (n + 1)! - 1",
"style": "rule"
} | {
"uid": "kd::ace641fd533b13ad7179ba42",
"index": "kd::ace641fd533b13ad7179ba42",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 23 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "The sum of the first $n$ terms of a sequence is $S_n = 2n^2 + n + 1$. Find the general formula for the sequence.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "a_n = \\begin{cases} 4 & \\text{if } n=1 \\ 4n - 2 & \\text{if } n \\geq 2 \\end{cases}",
"style": "rule"
} | {
"uid": "kd::04faf1a1720dca0cdc4f5d8c",
"index": "kd::04faf1a1720dca0cdc4f5d8c",
"lang": "en",
"rubrics": [
{
"criterion": "Use the relationship between the sum of terms and individual terms to express the general term as a difference of sums.",
"points": 2,
"tags": {
"judge": fal... |
t01_math | [
{
"role": "user",
"content": "Mariah intercovares 96 qt of milk from her farm. She pours 1/3 into containers and pours the remainder evenly into buckets. What is the number of quarts that each bucket holds?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"uid": "kd::0289eb16453781d53847ee33",
"index": "kd::0289eb16453781d53847ee33",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{96}{3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Sally starts with $50 in her piggy bank. The price of lollipops from The Royal Candy Store is $2.50. She wants to buy herself a $5 chocolate bar from The Royal Candy Store, but she only has exact change to pay for it. How many lollipops can Sally buy to pay for herself the choc... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"uid": "kd::51d95bff78cbb5fe1ab659df",
"index": "kd::51d95bff78cbb5fe1ab659df",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 45 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Theappledeep has 6 balls. Theappleridge has 4 times as many apples as theappledeep. Matt gives 2 apples to Sawyer and 6 apples to Gerald. Howmany apples remain in bothappleside houses?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
... | math | {
"ground_truth": "22",
"style": "rule"
} | {
"uid": "kd::8fc5762e72e69596346529f7",
"index": "kd::8fc5762e72e69596346529f7",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 24 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "When a plane climbs, it can reach a heightof 2000 feet in -40 seconds. What is the plane's rate in feet per second?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "50",
"style": "rule"
} | {
"uid": "kd::24af0b2106d29dc2045a616f",
"index": "kd::24af0b2106d29dc2045a616f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{2000\\div40}{1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gen... |
t01_math | [
{
"role": "user",
"content": "A particle moves along the $x$-axis according to the equation \\( s(t) = \\frac{1}{3} t^3 - t^2 - 8t + 12 \\), where \\( s \\) is the directed distance (in meters) of the particle from the origin at time \\( t \\) (in seconds). Find the time instant(s) when the particle is inst... | math | {
"ground_truth": "t = 4",
"style": "rule"
} | {
"uid": "kd::e644e95ec5a47dafd1c673fd",
"index": "kd::e644e95ec5a47dafd1c673fd",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{ds}{dt} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Calculate:<br/>$(1)\\sqrt{{{(-3)}^2}}+\\sqrt[3]{{-8}}-|π-2|$;<br/>$(2)\\frac{4}{3}÷{({-\\frac{1}{3}})^2}×({-\\frac{1}{2}})-{(-2)^2}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "-10",
"style": "rule"
} | {
"uid": "kd::58df084defe1a477822395d6",
"index": "kd::58df084defe1a477822395d6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\pi 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Let $X$ be a topological space where each connected component is open. Consider the sheaf $\\mathcal{O}_X$ associated with the constant presheaf $\\mathbb{Z}$. For an open subset $U$ of $X$, determine if $\\mathcal{O}_X(U) \\cong \\mathbb{Z}^i$, where $i$ is the number of conne... | math | {
"ground_truth": "True",
"style": "rule"
} | {
"uid": "kd::48584f46300f6cf24e805fb0",
"index": "kd::48584f46300f6cf24e805fb0",
"lang": "en",
"rubrics": [],
"rubric_profile": "math"
} |
t01_math | [
{
"role": "user",
"content": "Simplify \\(\\sqrt{16 j^{6}}\\), where \\( j \\) is a real number. Express your answer in simple radical form.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "4 j^{3}",
"style": "rule"
} | {
"uid": "kd::49465e44f4d4cbd17ab80211",
"index": "kd::49465e44f4d4cbd17ab80211",
"lang": "en",
"rubrics": [
{
"criterion": "Apply the product rule for radicals to separate the constant coefficient from the variable term.",
"points": 2,
"tags": {
"judge": false,
"inject": t... |
t01_math | [
{
"role": "user",
"content": "A factory is making tables. It will take 2 years to build the tables they want to make. After year, each table has a March representing the time they make it. If each March is 4 weeks long, how many weeks in total do they spend building tables?\n\nSolve the problem. Show your r... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"uid": "kd::a865e5ef219dd3f22522e1cd",
"index": "kd::a865e5ef219dd3f22522e1cd",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 48 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Let $G$ be a group acting on a finite set $X$ with $n$ elements. Prove that the order of $G$, denoted $|G|$, divides $n!$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "|G| divides n!",
"style": "rule"
} | {
"uid": "kd::aa04b23c832930217f9d9207",
"index": "kd::aa04b23c832930217f9d9207",
"lang": "en",
"rubrics": [],
"rubric_profile": "math"
} |
t01_math | [
{
"role": "user",
"content": "In the eighth grade, students organized a trip during the summer vacation, with 10 parent representatives joining the group. Travel agency A said: \"If all 10 parent representatives buy full-price tickets, the rest of the students can enjoy a half-price discount\"; Travel agenc... | math | {
"ground_truth": "x > 40",
"style": "rule"
} | {
"uid": "kd::cc7ca399a8030820820a0318",
"index": "kd::cc7ca399a8030820820a0318",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 400 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "The current population of Durban is 3,879,090, and the average rate of population growth in South Africa is 1.1% per annum. What can city planners expect the population of Durban to be in 6 years' time? Round your answer to the nearest integer.\n\nSolve the problem. Show your r... | math | {
"ground_truth": "4,142,255",
"style": "rule"
} | {
"uid": "kd::decbf95a0cfe449c41513408",
"index": "kd::decbf95a0cfe449c41513408",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 3879 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Andy wants to download as many song files as he can to play on his phone. He makes a 3 GB external USB drive for this purpose. The size of a typical song file is 40 MB. How many songs can 3 GB store?\n\nSolve the problem. Show your reasoning, then put the final answer inside ... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"uid": "kd::8e586e38e25bd77ca18426ca",
"index": "kd::8e586e38e25bd77ca18426ca",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 75 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Tom works 8 hours a week and earns $11 per hour. After a week, his total salary is twice the value of $80. In terms of $, how much does Spr HEALTH earn than Tom?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"uid": "kd::069cf081a20dc3a819f8ec46",
"index": "kd::069cf081a20dc3a819f8ec46",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 160 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Jessica painted a table once every 3 months. After 12 months how many of her paintings are permanent if each painting took up one half a wall?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::4f1ca0d85c93a6a8dda5c892",
"index": "kd::4f1ca0d85c93a6a8dda5c892",
"lang": "en",
"rubrics": [
{
"criterion": "Calculate the total number of painting sessions Jessica completes within the 12-month period.",
"points": 2,
"tags": {
"judge": false,
"inject": true... |
t01_math | [
{
"role": "user",
"content": "Susan has 21 cats and Bob has 3 cats. If Susan gives Robert x of her cats, how many more cats does Susan have than Bob?\nIf we know the answer to the above question is 14, what is the value of unknown variable x?\n\nSolve the problem. Show your reasoning, then put the final ans... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::5140d0e81f22e7a5ce17ebbe",
"index": "kd::5140d0e81f22e7a5ce17ebbe",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 18 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Given a prime number $p$, determine the number of generators for the cyclic group $\\mathbb{Z}_{p^r}$, where $r \\in \\mathbb{Z}, r \\geq 1$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "p^{r-1}(p-1)",
"style": "rule"
} | {
"uid": "kd::70d5e5147aa77ea01e3df7c9",
"index": "kd::70d5e5147aa77ea01e3df7c9",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{n}{\\gcd(an)} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gener... |
t01_math | [
{
"role": "user",
"content": "It takes George 10 minutes to get dressed in the morning. He also spends 2 minutes putting on his shoes and spends 5 minutes eating his breakfast. If George leaves his house at 10:45 in the morning, what time does he get to the bus stop?\n\nSolve the problem. Show your reasonin... | math | {
"ground_truth": "11:02 \\text{ AM}",
"style": "rule"
} | {
"uid": "kd::413f9f3366071804a476b72a",
"index": "kd::413f9f3366071804a476b72a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 17 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Sum of even numbers between 310 and 318?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "1570",
"style": "rule"
} | {
"uid": "kd::595dbec430f180552a204921",
"index": "kd::595dbec430f180552a204921",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 316 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Sean needs to replace 2 light bulbs in his bedroom, some in both the bathroom and the kitchen, and 4 in the basement. He also needs to replace 1/2 of that amount in the garage. The bulbs come 2 per pack. He will need 6 packs. How many light bulbs does he need to replace in both... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::d56b7e54bed45b157cc1faf1",
"index": "kd::d56b7e54bed45b157cc1faf1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "When Greg arrives at the second door with two empty glasses and goes up a flight of stairs that are exactly 117 feet high, he can lift them horizontally. Given that the total height of each vase is 2 inches, and one foot equals 12 inches, how many vases in total can he lift off... | math | {
"ground_truth": "702",
"style": "rule"
} | {
"uid": "kd::94c822a32fde29381e546ab4",
"index": "kd::94c822a32fde29381e546ab4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1404 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "In a certain state, 5% of the people are over 5 feet tall. If the state has a population of 1000, and 40% of the tall people drink milk, what is the total number of people throwing up milk?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"uid": "kd::f15d0e3a4953969f419e3162",
"index": "kd::f15d0e3a4953969f419e3162",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.05 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-\\sqrt{4}+{({-\\frac{1}{3}})^{-2}}+{(2017-\\sqrt{2})^0}$;<br/>$(2)\\frac{{2n-m}}{{m-n}}-\\frac{m}{{m-n}}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"uid": "kd::f0b2d9cd1f7349a1d5a0dc57",
"index": "kd::f0b2d9cd1f7349a1d5a0dc57",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{(2n-m)-m}{\\m-n} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "ge... |
t01_math | [
{
"role": "user",
"content": "Determine whether a radical ideal in a polynomial ring can contain only non-homogeneous elements.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "Yes",
"style": "rule"
} | {
"uid": "kd::af1419b101b6d20d334796df",
"index": "kd::af1419b101b6d20d334796df",
"lang": "en",
"rubrics": [],
"rubric_profile": "math"
} |
t01_math | [
{
"role": "user",
"content": "Noah everyone brought an apple to school today for snack. He bought enough that, after storing it in a roller holds the apples weighed 20 pounds. During the day he ate an apple he then ate out, which weighed 16 ounces. How many apples now weigh 20 pounds combined?\n\nSolve t... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"uid": "kd::68c0c72eabc15876a6d007be",
"index": "kd::68c0c72eabc15876a6d007be",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 21 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Juliana is making potion cubes for her gloves. Each potion cube has sides of size 3 inches. Knowing her gloves have a total surface area of 610 square inches, how many potion cubes must she create if each cube is used to cast the potion inside her gloves?\n\nSolve the problem. ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"uid": "kd::6a4a811212daed319008bcbe",
"index": "kd::6a4a811212daed319008bcbe",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 54 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Is a set \\( a \\) Dedekind-infinite if and only if \\( a \\) is infinite?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "Yes",
"style": "rule"
} | {
"uid": "kd::7d974e3bd655611ee8865fe3",
"index": "kd::7d974e3bd655611ee8865fe3",
"lang": "en",
"rubrics": [],
"rubric_profile": "math"
} |
t01_math | [
{
"role": "user",
"content": "There are no blackberries on the bushes in the forest to reach for a snack. You need to get some food so you make a triple soda tray of PB & J sandpockets (6 perforated pieces of 3 different varieties on each tray). How many trays do you need to pack if your goal is to make 2 p... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::bab842c6aecb80d4b9effd9e",
"index": "kd::bab842c6aecb80d4b9effd9e",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 18 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Mason collectedall the marbles out of his two boxes he store at home, which were found to have 8 blue marbles, 4 yellow marbles, 6 fell apart, and his friend gave him ten blue marbles. So Mason spent 2 minutes to count each of them until he came to a total. How many marbles did... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"uid": "kd::1bd34513e64044ac8bf578e4",
"index": "kd::1bd34513e64044ac8bf578e4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 18 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Daniel sends his doughnuts to a bakery. On Monday he sends 3 dozen doughnuts to their store, and decides to maintain that level of doughnut shipment every day, with the exception of Wednesday and Friday. On Wednesday, he sends three times the amount he did on Monday. On Frid... | math | {
"ground_truth": "252",
"style": "rule"
} | {
"uid": "kd::209ae10d9e03e792e013ec9d",
"index": "kd::209ae10d9e03e792e013ec9d",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 36 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Determine the highest power of 2 that divides \\(3^{1024} - 1\\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"uid": "kd::9235ef745c03093355315cf6",
"index": "kd::9235ef745c03093355315cf6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "A summer campfire can burn 400 square meters of land. It takes 1 hour to burn 16 quadrats, each having an area of 25 square meters. If 3 summer campires are weighed down by 300 humans, how many )\nYou are a helpful assistant.\n\nSolve the problem. Show your reasoning, then put ... | math | {
"ground_truth": "1200",
"style": "rule"
} | {
"uid": "kd::c2ba239409adaba6b5d11b3a",
"index": "kd::c2ba239409adaba6b5d11b3a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 48 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "다음 극한값을 구하시오: \\[ \\lim_{x \\rightarrow 0}\\frac{\\int_0^{\\sin x} (1+t)^{\\frac{1}{t}} dt}{x^2} \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "\\infty",
"style": "rule"
} | {
"uid": "kd::81433293c32f32ca0216c3b4",
"index": "kd::81433293c32f32ca0216c3b4",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 11 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "다음 극한을 구하시오: \\[ \\lim_{R \\to \\infty} \\int_0^R \\frac{\\cos x}{x^2} \\, dx \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "\\infty",
"style": "rule"
} | {
"uid": "kd::a7205762e56fcd70c49d880c",
"index": "kd::a7205762e56fcd70c49d880c",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 0.1 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "For what value of $a$ do the graphs of $y = ax^2 + 3x + 1$ and $y = -x - 1$ intersect at exactly one point?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::5c8f23c0897dab998ff46828",
"index": "kd::5c8f23c0897dab998ff46828",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 16 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "동치식 $4k \\equiv 4 \\pmod{16}$을 $k \\equiv \\text{어떤 수} \\pmod{16}$의 형태로 단순화하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "k \\equiv 1, 5, 9, 13 \\pmod{16}",
"style": "rule"
} | {
"uid": "kd::95ca1f11002a64865edd5856",
"index": "kd::95ca1f11002a64865edd5856",
"lang": "ko",
"rubrics": [],
"rubric_profile": "math"
} |
t01_math | [
{
"role": "user",
"content": "Consider a decreasing sequence of positive rational numbers \\((q_{n})_{n\\in\\mathbb{Z}_{> 0}}\\), where each term is given by \\(q_n = \\frac{n_{i}}{d_{i}}\\) with \\((n_{i},d_{i})=1\\) for all \\(i\\). The sequence has the property that if \\(i \\neq j\\), then \\((n_{i}d_{i... | math | {
"ground_truth": "Yes",
"style": "rule"
} | {
"uid": "kd::c7902c29c1c6b5e7949387e0",
"index": "kd::c7902c29c1c6b5e7949387e0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{d_{i}} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "On the first day, there are 200 cold medial tokens on the utility's pool and the price is $0.25 per token. On the second day, there are 300 seemingly verified (Medal) tokens on the pool, and the price is $0.4 per token. On the third day, there are 400 cold medial tokens and the... | math | {
"ground_truth": "2210",
"style": "rule"
} | {
"uid": "kd::08b45e5c6b1b7c55043ec3ce",
"index": "kd::08b45e5c6b1b7c55043ec3ce",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 50 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "How many integers between $900$ and $1000$ have all three of the numbers $15$, $20$, and $25$ as factors?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"uid": "kd::21a21eb2523d9a1f81176c1b",
"index": "kd::21a21eb2523d9a1f81176c1b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 60 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "How can I prove that the limit of $$\\lim_{n\\to\\infty}\\left(\\sqrt{n^2+(-1)^n}-n\\right)$$ does not exist?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::05adf5ee65d6590706eb6b63",
"index": "kd::05adf5ee65d6590706eb6b63",
"lang": "en",
"rubrics": [
{
"criterion": "Rationalize the expression by multiplying the numerator and denominator by the conjugate sum.",
"points": 2,
"tags": {
"judge": false,
"inject": true... |
t01_math | [
{
"role": "user",
"content": "양의 정수에 각각 7을 더하여 만든 수열에서 연속된 네 정수의 합이 238일 때, 이 네 정수의 합을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "210",
"style": "rule"
} | {
"uid": "kd::92799a9a6512879c81deb3d5",
"index": "kd::92799a9a6512879c81deb3d5",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 105 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Elizabeth just finished a job. She raised $200 working part time and received $4 more than 2 times this amount a half-hour job she completed. For the second job, she received times twice this amount for working three times longer. She spent $1,200 on vest and gloves for her new... | math | {
"ground_truth": "212",
"style": "rule"
} | {
"uid": "kd::1055b706ea5ef2f46115a699",
"index": "kd::1055b706ea5ef2f46115a699",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Find the sum of the prime factors of 539.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"uid": "kd::9fd27ff4b7ba5a2204953c56",
"index": "kd::9fd27ff4b7ba5a2204953c56",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 490 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Determine the intersection of the third element of the sequence of sets \\( \\left(\\left\\{ A\\in\\mathcal{M}_2\\left(\\mathbb{R} \\right) | A^{n+1} =2003^nA\\right\\}\\right)_{n\\ge 1} \\) with the 2003rd element.\n\nSolve the problem. Show your reasoning, then put the final... | math | {
"ground_truth": "S_3\\cap S_{2003} =\\{A\\in\\mathcal M_2(\\mathbb R)\\mid A^2=2003A\\} =\\{2003P | P\\in\\mathcal M_2(\\mathbb R), P^2=P\\}",
"style": "rule"
} | {
"uid": "kd::194ff5165a7336fccd3a1139",
"index": "kd::194ff5165a7336fccd3a1139",
"lang": "en",
"rubrics": [
{
"criterion": "Determine the set of matrices that simultaneously satisfy both polynomial equations derived from the sequence definition.",
"points": 2,
"tags": {
"judge": f... |
t01_math | [
{
"role": "user",
"content": "A water ride at an amusement park takes 3 seconds to start. After starting, theActual water ride takes exactly half the ride time of the water ride with the least time. The water ride with the least time takes 7 seconds longer than the initial ride start time. How long does t... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::630c070ded2408a5d8480277",
"index": "kd::630c070ded2408a5d8480277",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Simplify the following expressions:\n(a) $18(-4) \\div(-2)^{3}$ \n(b) $-32 \\div 4+(-2)(-7)$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::dbe0ee8abee7786424e997a0",
"index": "kd::dbe0ee8abee7786424e997a0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -72 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Martin makes twice the amount of soda water that Sally makes. He made 400L of soda water and Sally also produced a certain amount of soda water. If Sally produces L liters of soda water to match the amount Martin produces, what is L in liters?\n\nSolve the problem. Show your re... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"uid": "kd::b2510f94b96aabd9c7637162",
"index": "kd::b2510f94b96aabd9c7637162",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{400}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Denny buys half of the bank's services which cost $50000. Then twice as much as he does t buy more of their products. How much does he pay for all the services together?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "75000",
"style": "rule"
} | {
"uid": "kd::efed42703945898b1d147e30",
"index": "kd::efed42703945898b1d147e30",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "You are selling your house for $1,500,000. You have constructed an addition to your house that has a loft and a sunroom but both cost $150,000. You also have to pay $120,000 in property taxes, $50,000 in fees, and a one-time closing cost of $125,500. How much profit do you m... | math | {
"ground_truth": "904500",
"style": "rule"
} | {
"uid": "kd::1e8ba9acff3d8283f898fcf0",
"index": "kd::1e8ba9acff3d8283f898fcf0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 595500 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Charlotte had 6 jars of jam after making some. She consumed total of 1/3, doubled up the quantity on biscuits, and then subtracted 4 from the rest. How many jars of jam remained?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::8575ccd97f699954d6d25ab7",
"index": "kd::8575ccd97f699954d6d25ab7",
"lang": "en",
"rubrics": [
{
"criterion": "Track the number of jars through each sequential operation described in the problem statement.",
"points": 2,
"tags": {
"judge": false,
"inject": tru... |
t01_math | [
{
"role": "user",
"content": "Find all real numbers \\( x \\) and \\( a \\) that satisfy the equation \\( x^3 + a^3 = x^2 - ax + a^2 \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "x = 1 - a",
"style": "rule"
} | {
"uid": "kd::707923d3048dd12a02f32f34",
"index": "kd::707923d3048dd12a02f32f34",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "I translated a sum of terms being multiplied into a single summation, but I'm not sure if the summation I've made matches the sum I originally had.\n\nOriginal Equation: $\\frac{26!}{8!(26-8)!} + \\frac{26!}{7!(26-7)!}(\\frac{26!}{1!(26-1)!}) + \\frac{26!}{6!(26-6)!}(\\frac{26!... | math | {
"ground_truth": "264517825",
"style": "rule"
} | {
"uid": "kd::dd3023e0bd4a1ae00d6001df",
"index": "kd::dd3023e0bd4a1ae00d6001df",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Is it necessary for the function $V(x)$ to be an even function if both $g(x)$ and $g(-x)$ are solutions to the differential equation $kf_{xx} + V(x)f(x) = cf(x)$, where $k$ is a negative constant and $c$ is a constant?\n\nSolve the problem. Show your reasoning, then put the fin... | math | {
"ground_truth": "Yes",
"style": "rule"
} | {
"uid": "kd::48fc02c6c3fa1e3074fc8682",
"index": "kd::48fc02c6c3fa1e3074fc8682",
"lang": "en",
"rubrics": [],
"rubric_profile": "math"
} |
t01_math | [
{
"role": "user",
"content": "희소(sparse), 대칭, 양정치(positive definite) 행렬 $A$에 대해 선형 방정식 계 $Ax = b$를 푸는 켤레 기울기법(conjugate gradient method)의 시간 복잡도를 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "O(n^2)",
"style": "rule"
} | {
"uid": "kd::142338d8ad357a454b0d637b",
"index": "kd::142338d8ad357a454b0d637b",
"lang": "ko",
"rubrics": [
{
"criterion": "각 반복 단계에서 수행되는 행렬 벡터 곱셈과 벡터 연산의 계산 비용을 분석하여 단일 반복의 시간 복잡도를 구하라.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold_rank": 1,
... |
t01_math | [
{
"role": "user",
"content": "What is the product of $-235\\times243\\times250?$\nCompute $\\text{LCM}(22,58).$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "638",
"style": "rule"
} | {
"uid": "kd::e0ef3e56b167f2c71e2fa1bc",
"index": "kd::e0ef3e56b167f2c71e2fa1bc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 48 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "If a function $g(x_1, x_2, ..., x_n)$ is anti-symmetric in $x_2$, prove or disprove that the integral of $g$ over a region symmetric with respect to $x_2$ is equal to 0.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::b86cf383a34bf141ea401746",
"index": "kd::b86cf383a34bf141ea401746",
"lang": "en",
"rubrics": [],
"rubric_profile": "math"
} |
t01_math | [
{
"role": "user",
"content": "아담의 옷장이 너무 붐비므로 그는 자선 가게에 일부 옷을 기부하기로 결정한다. 그는 바지 4벌, 스웨터 4벌, 파자마 세트(상하의) 4세트, 그리고 몇 벌의 티셔츠를 꺼내 친구들에게 기부할 물건이 있는지 묻는다. 그의 친구 3명은 각각 아담과 같은 양의 옷을 기부한다. 이후 그는 자신의 옷을 다시 살펴보다가 실제로는 자신의 옷의 절반을 유지하고 싶다고 결정한다. 총 126벌의 옷이 기부된다. 아담이 처음에 꺼낸 티셔츠는 몇 벌인가?\n\nSolve the problem. Show your re... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"uid": "kd::9c22ab945a1daa6a2990bf37",
"index": "kd::9c22ab945a1daa6a2990bf37",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 63 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "\\( k \\)가 무한대로 갈 때 급수 \\( \\sum_{n=1}^{\\infty}\\frac{1}{n^k+1} \\)가 \\( \\frac{1}{2} \\)로 수렴하는지 판별하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"uid": "kd::cf2a7e4e564530b50a5afe67",
"index": "kd::cf2a7e4e564530b50a5afe67",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{n^{k}+1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic... |
t01_math | [
{
"role": "user",
"content": "Calculate the total work required to pump all the water out of a cylindrical tank with a radius of 2 meters and a length of 10 meters. Assume the tank is filled with water, the acceleration due to gravity is 9.8 m/s², and the density of water is 1000 kg/m³. Express your answer ... | math | {
"ground_truth": "784000\\pi",
"style": "rule"
} | {
"uid": "kd::ac8979ffe6f1acc945894a44",
"index": "kd::ac8979ffe6f1acc945894a44",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 500 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Francisca can run 5 mph on the treadmill while John can run 9 mph. How much faster can Francisca run than John?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::0834168f512ad44e2005683e",
"index": "kd::0834168f512ad44e2005683e",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the two given running speeds and determine which value is larger to find the difference.",
"points": 2,
"tags": {
"judge": false,
"inject": ... |
t01_math | [
{
"role": "user",
"content": "Is there a finite group $G$ of order $p(p^2-1)$ that has a normal subgroup $N$ such that $G/N \\cong PSL(2, p)$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "Yes",
"style": "rule"
} | {
"uid": "kd::cfb7ff473b90f8c62e68ed80",
"index": "kd::cfb7ff473b90f8c62e68ed80",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 24 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Determine whether the function \\( f(x, y) = \\frac{y^2 \\sin x}{x^2 + y^2} \\) is continuous at the point (0,0).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "Yes",
"style": "rule"
} | {
"uid": "kd::22134b66d54bca2f8736886d",
"index": "kd::22134b66d54bca2f8736886d",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{y^{2}\\sinx}{x^{2}+y^{2}} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_k... |
t01_math | [
{
"role": "user",
"content": "Let \\( U = \\{(x, y, x + y, x - y, 2x) \\in F^5 \\mid x, y \\in F\\} \\). Find three subspaces \\( W_1, W_2, W_3 \\) of \\( F^5 \\), none of which equals \\(\\{0\\}\\), such that \\( F^5 = U \\oplus W_1 \\oplus W_2 \\oplus W_3 \\).\n\nSolve the problem. Show your reasoning, th... | math | {
"ground_truth": "W_1 = \\operatorname{span}\\{(0,0,1,0,0)\\}, W_2 = \\operatorname{span}\\{(0,0,0,1,0)\\}, W_3 = \\operatorname{span}\\{(0,0,0,0,1)\\}",
"style": "rule"
} | {
"uid": "kd::24bb8a43e169a4e84da50795",
"index": "kd::24bb8a43e169a4e84da50795",
"lang": "en",
"rubrics": [
{
"criterion": "Determine the dimension of U by finding a basis for the given parametric definition.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "Peter buys 2 new cars and 1 van. His car costs $25,000 and his van costs $10,000. He also needs to replace the bumper on the van for $400 and he needs to build this bumper by hand for 50 hours and earn $8.00 per hour. How much did he pay to replace the bumper to hand build i... | math | {
"ground_truth": "800",
"style": "rule"
} | {
"uid": "kd::537f8ed71c779475fe1727f5",
"index": "kd::537f8ed71c779475fe1727f5",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 40 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "비음의 가측 함수 $f: X \\rightarrow \\mathbb{R}$과 $\\mu(A) = 0$인 집합 $A$가 주어졌을 때, $\\int_A f \\, d\\mu = 0$이 성립하는지 판별하고 그 이유를 설명하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::c6a135fac52e26944e8c4119",
"index": "kd::c6a135fac52e26944e8c4119",
"lang": "ko",
"rubrics": [
{
"criterion": "비음 가측 함수의 적분을 단순 함수의 상한으로 정의하는 방식을 활용하여 접근하라",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold_rank": 1,
"scaffold_k... |
t01_math | [
{
"role": "user",
"content": "The range of 6 flips of a balance coin is which among the following options?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::a1b6c322f7ff6db5788377af",
"index": "kd::a1b6c322f7ff6db5788377af",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the minimum and maximum possible counts of heads in six coin flips.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffo... |
t01_math | [
{
"role": "user",
"content": "대칭 행렬 $A \\in \\mathbb{R}^{n \\times n}$과 벡터 $x \\in \\mathbb{R}^n$에 대하여, 식 $x^T A x$의 야코비 행렬을 $A$와 $x$를 사용하여 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "2x^T A",
"style": "rule"
} | {
"uid": "kd::6cd421ffe941c700eb7b80b1",
"index": "kd::6cd421ffe941c700eb7b80b1",
"lang": "ko",
"rubrics": [
{
"criterion": "스칼라 함수의 야코비 행렬이 그 기울기 벡터의 전치행렬임을 이용하여 접근하라",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold_rank": 1,
"scaffold_kin... |
t01_math | [
{
"role": "user",
"content": "What is the other endpoint of the segment with end points (7,3) and (4,-5)?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "(1, -13)",
"style": "rule"
} | {
"uid": "kd::0b18fe7a908ce34c887165f5",
"index": "kd::0b18fe7a908ce34c887165f5",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Bill bought a group of coconuts, 3 of them were empty and 17 were bad. the rest were full of coconut milk with equal amounts of water, leaving 10 coconuts after enough water was squeezed out of each to make them smooth. how many coconuts did Bill believe in?\n\nSolve the proble... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"uid": "kd::8813c1c4a668737738c52ed4",
"index": "kd::8813c1c4a668737738c52ed4",
"lang": "en",
"rubrics": [
{
"criterion": "Define a variable for the total number of coconuts and subtract the known defective groups to find the count of full coconuts.",
"points": 2,
"tags": {
"judg... |
t01_math | [
{
"role": "user",
"content": "What is the value of the prime-counting function `pi(10)`, which counts the number of primes less than or equal to 10? Compute `pi(10) - 10` and compare this result to `1/ln(10)` using a calculator.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\b... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::b43e74a5b72e1ad2774ea46a",
"index": "kd::b43e74a5b72e1ad2774ea46a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.434294 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Simplify:\\[\\left[\\left(0.25\\times4\\right)\\times10-3\\right]\\p\\frac{7}{10}\\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::0649cde506eb730bb98a02c3",
"index": "kd::0649cde506eb730bb98a02c3",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 77 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "What is a common factor of 24 and 48 which is not a factor of 12?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"uid": "kd::6a59335c11889454369500e4",
"index": "kd::6a59335c11889454369500e4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "극한 \\( \\lim_{x\\to 0}\\left(\\frac{(-2)^{\\lfloor x \\rfloor}}{x} \\right) \\)의 존재 여부를 판별하고, 존재한다면 그 값을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}."
}
] | math | {
"ground_truth": "\\infty",
"style": "rule"
} | {
"uid": "kd::84377c75367bf9ec52452ce4",
"index": "kd::84377c75367bf9ec52452ce4",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{2|x|} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
End of preview. Expand in Data Studio
수학 RL 학습 데이터 — 응답 예산별 3묶음
폴더 하나만 받으면 됩니다. 학습에 쓸 응답 길이 상한에 맞는 폴더를 고르세요. 각 폴더는 그 자체로 완결이고, 데이터·리워드·루브릭이 모두 들어 있습니다.
| 폴더 | 응답 상한 | 문제 수 | 이 예산에서 늘어난 분 | 힌트판 | 루브릭 보유 |
|---|---|---|---|---|---|
to-16k/ |
16,384 | 2,429 | +2,429 | 2,069 | 2,313 |
to-32k/ |
32,768 | 5,542 | +3,113 | 4,245 | 5,072 |
to-64k/ |
65,536 | 6,455 | +913 | 4,245 | 5,724 |
폴더는 누적입니다. to-32k/ 는 to-16k/ 의 문제를 포함합니다.
응답 32,768 로 학습한다면 to-32k/ 하나만 받으면 됩니다.
구간 전용도 따로 있습니다 — bands/
누적이 아니라 그 구간에서 처음 learnable 이 되는 문제만 담았습니다.
세 파일을 합치면 to-64k/ 와 같아집니다.
| 파일 | 구간 | 문제 | 힌트판 | 루브릭 |
|---|---|---|---|---|
bands/upto-16k.parquet |
~16K | 2,429 | 2,069 | 2,313 |
bands/16k-to-32k.parquet |
16K~32K | 3,113 | 2,176 | 2,759 |
bands/32k-to-64k.parquet |
32K~64K | 913 | 0 | 652 |
힌트판은 bands/<구간>_hint.parquet 입니다. 루브릭과 리워드는 to-* 폴더 것을 그대로 쓰면 됩니다.
학습에 바로 쓰실 거면 to-* 를, 구간별 효과를 비교하실 거면 bands/ 를 보세요.
폴더 안 구조
to-32k/
├── data/
│ ├── train.parquet 일반 프롬프트 · bin·partial 케이스가 함께 씀
│ ├── train_hint.parquet 교사 힌트를 프롬프트에 넣은 판 · hint 케이스용
│ └── val_45.parquet 검증 45문제 (세 폴더 동일)
├── reward/
│ ├── bin.py 이진 정답 리워드
│ └── partial.py 부분점수 리워드
├── rubrics/
│ └── rubric.jsonl 이 폴더에 든 문제의 루브릭만
└── cases.json 케이스 3종의 데이터·리워드·환경변수
케이스 3종
| 케이스 | 데이터 | 리워드 | 환경변수 |
|---|---|---|---|
bin |
data/train.parquet |
reward/bin.py |
T01_LADDER=0 T01_LADDER_KIND=0 T01_PARTIAL=0 |
partial |
data/train.parquet |
reward/partial.py |
T01_LADDER=0.1 T01_LADDER_KIND=0.05 T01_PARTIAL=0.3 |
hint |
data/train_hint.parquet |
reward/bin.py |
bin 과 같음 |
폴더 3개 × 케이스 3종 = 9가지 조합입니다.
어떻게 고른 문제인가
대상 모델 Qwen3.5-35B-A3B(thinking)로 후보 풀을 K=4 이상, temp 0.7 · top-p 0.95 로 직접 풀려 보고, 그 모델이 풀다 말다 하는 문제만 남겼습니다.
- 잘린 표본의 정답은 인정하지 않습니다
- 완주한 표본 중에 정답과 오답이 모두 있어야 채택합니다 (GRPO 그룹 안에 분산이 생겨야 학습이 됩니다)
- 응답 상한을 바꾸면 무엇이 잘렸는지가 달라지므로 채택 집합도 달라집니다. 폴더를 나눈 이유가 이것입니다
붙이는 법
reward_model.ground_truth = ground_truth (answer 아님)
extra_info.index = uid
extra_info.rubrics = rubrics (행 안의 list 그대로)
custom_reward_function.path = reward/bin.py 또는 reward/partial.py
custom_reward_function.name = compute_score_dict
calculate_log_probs=False · static_pack 지정 금지
루브릭은 데이터 행 안에도 있고 rubrics/rubric.jsonl 에 uid 색인으로도 있습니다.
둘은 같은 원본에서 쓰므로 항상 일치합니다.
주의
- 학습 응답 상한은 폴더 이름과 같게 맞춰야 판정이 맞습니다
- 루브릭이 없는 행이 일부 있습니다.
bin케이스는 루브릭을 보상에 쓰지 않아 영향이 없고,partial과hint는 루브릭 보유 행만 쓰면 됩니다 - 검증 45문제는 세 폴더에 같은 파일로 들어 있습니다. 학습 데이터와 겹치지 않습니다
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