prompt listlengths 1 1 | label stringlengths 1 10.8M | domain stringclasses 3
values | teacher stringclasses 3
values | metadata dict |
|---|---|---|---|---|
[
{
"role": "user",
"content": "You're playing a video game, in which you will get an achievement if you complete all of the levels consecutively without dying. You can play the levels in any order, and each time you play a level you'll either complete it or die. Each level has some probability that you'll co... | {"inputs": ["1\n4\n1 1 1 1\n50 0 20 20\n\nSAMPLE", "1\n4\n1 1 1 1\n50 0 20 20", "3\n4\n1 1 1 1\n50 0 20 20\n3\n100 10 1\n0 50 0\n3\n100 80 50\n40 20 80", "1\n4\n1 1 1 1\n50 0 6 20", "3\n4\n1 1 1 1\n50 0 20 20\n3\n100 10 1\n0 50 0\n3\n100 80 50\n34 20 80", "1\n4\n1 1 1 1\n50 0 20 20\n\nTAMPLE", "3\n4\n1 1 1 1\n50 0 20 2... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 19261
} |
[
{
"role": "user",
"content": "Let $T$ be an isomorphism acting on a separable Banach space $X$. Determine whether there always exists a countable dense subset $D$ of $X$ such that $T(D) = D$. Provide a proof or counterexample.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 20006
} |
[
{
"role": "user",
"content": "Write a short note to a friend about the last day of summer.\n\nFollow ALL of these requirements exactly:\n- Do not use any commas.\n- Wrap your entire answer in << and >>."
}
] | [{"type": "no_commas"}, {"type": "wrapped_in", "open": "<<", "close": ">>"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 3411
} |
[
{
"role": "user",
"content": "Write a short note to a friend about a birthday without cake.\n\nFollow ALL of these requirements exactly:\n- Answer in exactly 4 sentences."
}
] | [{"type": "sentence_count", "n": 4}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 7328
} |
[
{
"role": "user",
"content": "Explain a garden fence to someone who has never encountered it.\n\nFollow ALL of these requirements exactly:\n- Answer as exactly 4 numbered items, like '1. '.\n- Begin by repeating this exactly: \"Explain a garden fence to someone who has never encountered it.\""
}
] | [{"type": "numbered_count", "n": 4}, {"type": "repeat_first", "value": "Explain a garden fence to someone who has never encountered it."}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 7708
} |
[
{
"role": "user",
"content": "Explain why someone might find a walk before dawn memorable.\n\nFollow ALL of these requirements exactly:\n- Begin your answer with \"Answer:\"."
}
] | [{"type": "starts_with", "value": "Answer:"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1597
} |
[
{
"role": "user",
"content": "One day, n people (n is an even number) met on a plaza and made two round dances, each round dance consists of exactly n/2 people. Your task is to find the number of ways n people can make two round dances if each round dance consists of exactly n/2 people. Each person should b... | {"inputs": ["2\n", "20\n", "4\n", "8\n", "14\n", "16\n", "18\n", "6\n", "10\n", "12\n", "010\n"], "outputs": ["1\n", "12164510040883200\n", "3\n", "1260\n", "889574400\n", "163459296000\n", "39520825344000\n", "40\n", "72576\n", "6652800\n", "72576\n"]} | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 4398
} |
[
{
"role": "user",
"content": "Write a short description of the hum of power lines.\n\nFollow ALL of these requirements exactly:\n- Write your entire answer in capital letters.\n- Include at least 2 placeholders in square brackets, like [name]."
}
] | [{"type": "all_caps"}, {"type": "placeholder_count", "n": 2}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 7109
} |
[
{
"role": "user",
"content": "Write a short note to a friend about a fallen branch.\n\nFollow ALL of these requirements exactly:\n- Answer in exactly 2 paragraphs separated by a blank line.\n- Use at most 160 words.\n- Do not use the letter 'a' anywhere."
}
] | [{"type": "paragraph_count", "n": 2}, {"type": "word_count_max", "n": 160}, {"type": "forbidden_chars", "values": ["a"]}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 99
} |
[
{
"role": "user",
"content": "Summarise what matters most about how thermometers work.\n\nFollow ALL of these requirements exactly:\n- End your answer with \"THE END\".\n- Your answer must not contain the word \"gravity\"."
}
] | [{"type": "ends_with", "value": "THE END"}, {"type": "must_exclude", "values": ["gravity"]}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1260
} |
[
{
"role": "user",
"content": "Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that for all real numbers \\( x \\) and \\( y \\), the equation \\( f(x^2+y) = xf(x) + f(y) \\) holds.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | f(x) = kx | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 21239
} |
[
{
"role": "user",
"content": "Chef plays with the sequence of N numbers. During a single move Chef is able to choose a non-decreasing subsequence of the sequence and to remove it from the sequence. Help him to remove all the numbers in the minimal number of moves. \n\nInput\nThe first line of each test case... | {"inputs": ["3 \n1 2 3", "4\n4 1 2 3", "3 \n1 2 5", "4\n4 1 3 3", "3 \n5 1 0", "4\n20 -1 -2 -4", "3 \n1 2 8", "4\n4 1 5 3", "3 \n1 1 8", "4\n4 0 5 3", "3 \n1 1 16", "4\n4 -1 5 3", "3 \n2 1 16", "4\n4 -1 5 4", "3 \n2 1 3", "4\n1 -1 5 4", "3 \n2 1 5", "4\n1 -1 5 7", "3 \n2 2 5", "4\n0 -1 5 7", "3 \n2 3 5", "4\n0 -1 5 8",... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 16302
} |
[
{
"role": "user",
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\left(\\sum_{k=0}^{n-1}(\\zeta(2)-H_{k,2})-H_n\\right) \\] where \\( H_{k,2}:=\\sum_{j=1}^k\\frac1{j^2} \\).\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 1 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 13526
} |
[
{
"role": "user",
"content": "We will play a one-player game using a number line and N pieces.\n\nFirst, we place each of these pieces at some integer coordinate.\n\nHere, multiple pieces can be placed at the same coordinate.\n\nOur objective is to visit all of the M coordinates X_1, X_2, ..., X_M with thes... | {"inputs": ["3 7\n-10 -3 0 9 -100 2 17", "2 5\n10 12 1 2 14", "100 1\n-100000", "3 7\n-10 -1 0 9 -100 2 17", "100 1\n-151489", "3 7\n-8 -1 0 9 -100 2 17", "3 7\n-10 -3 0 9 -100 2 18", "2 5\n10 12 1 4 14", "6 7\n-8 -1 0 9 -100 2 17", "2 5\n10 12 1 4 21", "2 7\n-8 -1 0 9 -100 2 17", "3 7\n-10 -3 0 9 -5 0 17", "3 7\n-8 -1... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 22192
} |
[
{
"role": "user",
"content": "Calculate the volume of the solid enclosed by the surfaces $z = x^2$ and $z = 4 - x^2 - y^2$. The projection of the solid onto the $xy$-plane is an ellipse given by the equation $\\frac{x^2}{2} + \\frac{y^2}{4} = 1$. Express the volume $V$ as an integral and evaluate it.\nPleas... | 4\sqrt{2}\pi | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 39777
} |
[
{
"role": "user",
"content": "Evaluate the integral: $$\\int_{0}^{2\\pi} e^{i\\cos\\theta}\\cos\\theta \\, d\\theta$$\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 2\pi i J_1(1) | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 43226
} |
[
{
"role": "user",
"content": "You are given a string s of even length n. String s is binary, in other words, consists only of 0's and 1's.\n\nString s has exactly n/2 zeroes and n/2 ones (n is even).\n\nIn one operation you can reverse any substring of s. A substring of a string is a contiguous subsequence ... | {"inputs": ["3\n2\n10\n4\n0110\n8\n11101000\n", "3\n2\n10\n4\n0110\n8\n11100001\n", "3\n2\n10\n4\n1010\n8\n11101000\n", "3\n2\n10\n4\n0011\n8\n11101000\n", "3\n2\n10\n4\n0101\n8\n11100001\n", "3\n2\n10\n4\n0101\n8\n11101000\n", "3\n2\n10\n4\n0011\n8\n11100001\n", "3\n2\n10\n4\n1001\n8\n11101000\n", "3\n2\n10\n4\n0011\n... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 15076
} |
[
{
"role": "user",
"content": "Write a short description of a postcard that arrived late.\n\nFollow ALL of these requirements exactly:\n- Answer in exactly 2 paragraphs separated by a blank line.\n- Begin your answer with \"In short:\".\n- Answer in exactly 2 sentences."
}
] | [{"type": "paragraph_count", "n": 2}, {"type": "starts_with", "value": "In short:"}, {"type": "sentence_count", "n": 2}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 4237
} |
[
{
"role": "user",
"content": "Ujan decided to make a new wooden roof for the house. He has $n$ rectangular planks numbered from $1$ to $n$. The $i$-th plank has size $a_i \\times 1$ (that is, the width is $1$ and the height is $a_i$).\n\nNow, Ujan wants to make a square roof. He will first choose some of th... | {
"inputs": [
"4\n5\n4 3 1 4 5\n4\n4 4 4 4\n3\n1 1 1\n5\n5 5 1 1 5\n",
"10\n1\n1\n2\n2 1\n3\n3 1 2\n3\n2 2 2\n4\n4 1 4 1\n5\n5 4 3 2 1\n5\n1 2 3 4 5\n6\n3 2 1 6 2 2\n10\n4 5 2 9 6 10 3 7 1 8\n10\n1 3 2 2 2 9 10 10 9 7\n"
],
"outputs": [
"3\n4\n1\n3\n",
"1\n1\n2\n2\n2\n3\n3\n2\n5\n5\n"
]
} | code | code | {
"domain": "code",
"data_source": "apps",
"src_index": 10481
} |
[
{
"role": "user",
"content": "Vitya has just started learning Berlanese language. It is known that Berlanese uses the Latin alphabet. Vowel letters are \"a\", \"o\", \"u\", \"i\", and \"e\". Other letters are consonant.\n\nIn Berlanese, there has to be a vowel after every consonant, but there can be any let... | {"inputs": ["codeforces\n", "ninja\n", "sumimasen\n", "s\n", "d\n", "anujemogawautiedoneobninnibonuunaoennnyoorufonxionntinimiboonununnnnnleenqunminzayoutanlalo\n", "uixinnepnlinqaingieianndeakuniooudidonnnqeaituioeneiroionxuowudiooonayenfeonuino\n", "king\n", "z\n", "yy\n", "aaz\n", "nbaaaaaaaa\n", "pya\n", "aeionnhhh... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 14432
} |
[
{
"role": "user",
"content": "Give practical advice about how compasses point north.\n\nFollow ALL of these requirements exactly:\n- Your answer must not contain the word \"orange\", the word \"market\".\n- Wrap your entire answer in << and >>."
}
] | [{"type": "must_exclude", "values": ["orange", "market"]}, {"type": "wrapped_in", "open": "<<", "close": ">>"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 5399
} |
[
{
"role": "user",
"content": "Phoenix loves playing with bits — specifically, by using the bitwise operations AND, OR, and XOR. He has n integers a_1, a_2, ..., a_n, and will perform q of the following queries:\n\n 1. replace all numbers a_i where l ≤ a_i ≤ r with a_i AND x; \n 2. replace all numbers a_i ... | {"inputs": ["6 7\n6 0 2 3 2 7\n1 0 4 3\n2 6 8 4\n4 0 7\n3 2 5 3\n1 0 1 2\n4 0 3\n4 2 7\n", "5 6\n5 4 3 2 1\n1 2 3 2\n4 2 5\n3 2 5 3\n4 1 6\n2 1 1 8\n4 8 10\n", "5 5\n2 0 5 2 0\n3 4 4 4\n4 1 5\n1 0 0 5\n3 3 4 1\n4 1 3\n", "5 5\n51989 112699 641265 904734 417105\n1 333773 405840 487648\n1 252510 429994 534513\n4 308328 3... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 22940
} |
[
{
"role": "user",
"content": "Description\n\nSince the cubic equation: ax ^ 3 + bx ^ 2 + cx + d = 0 is given, please check the number of positive real roots and the number of negative real roots, respectively.\n\nThe number of roots shall be counted including the multiple roots.\n\n\n\nInput\n\nThe input co... | {"inputs": ["2\n1 3 3 1\n-10 0 0 1", "2\n1 4 3 1\n-14 0 0 1", "2\n1 3 5 1\n-10 0 0 0", "2\n1 3 9 1\n-10 0 1 0", "2\n1 4 3 0\n-1 0 1 1", "2\n1 1 3 1\n-10 -1 0 0", "2\n1 4 3 0\n-1 -1 1 1", "2\n1 4 3 0\n-1 0 0 0", "2\n1 4 3 0\n-1 0 1 0", "2\n2 4 3 0\n-1 0 1 0", "2\n1 0 0 1\n-1 -10 3 1", "2\n1 -1 -1 1\n-1 -10 3 1", "2\n1 3... | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 21997
} |
[
{
"role": "user",
"content": "Evaluate the integral: \\[ \\int_{0}^{2\\pi} \\frac{\\cos(3\\theta)}{5-4\\cos(\\theta)}d\\theta \\] without using the residue theorem.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | \dfrac{\pi}{12} | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 5610
} |
[
{
"role": "user",
"content": "Given a non-negative real-valued function $f(n)$ defined for all natural numbers $n$, if $f$ is convex and $\\lim_{n\\to\\infty}f(n)$ exists as a finite number, must $f$ be non-increasing? Answer yes or no.\nPlease reason step by step, and put your final answer within \\boxed{}... | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 37664
} |
[
{
"role": "user",
"content": "Describe a bicycle repair without using technical jargon.\n\nFollow ALL of these requirements exactly:\n- Include at least 1 placeholders in square brackets, like [name].\n- Answer as exactly 4 bullet points, each starting with '- '.\n- Your answer must contain the word \"marke... | [{"type": "placeholder_count", "n": 1}, {"type": "bullet_count", "n": 4}, {"type": "must_include", "values": ["market", "lantern"]}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1458
} |
[
{
"role": "user",
"content": "Summarise what matters most about learning to cook.\n\nFollow ALL of these requirements exactly:\n- Reply with valid JSON and nothing else.\n- Do not use any commas."
}
] | [{"type": "valid_json"}, {"type": "no_commas"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 7314
} |
[
{
"role": "user",
"content": "Describe an orchard in spring without using technical jargon.\n\nFollow ALL of these requirements exactly:\n- Answer in exactly 2 paragraphs separated by a blank line.\n- Write your entire answer in lowercase letters only."
}
] | [{"type": "paragraph_count", "n": 2}, {"type": "all_lowercase"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 3709
} |
[
{
"role": "user",
"content": "Describe a foghorn at night as it would appear to a first-time visitor.\n\nFollow ALL of these requirements exactly:\n- End your answer with \"-- done --\".\n- Answer as exactly 2 numbered items, like '1. '."
}
] | [{"type": "ends_with", "value": "-- done --"}, {"type": "numbered_count", "n": 2}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 4438
} |
[
{
"role": "user",
"content": "Stepan likes to repeat vowel letters when he writes words. For example, instead of the word \"pobeda\" he can write \"pobeeeedaaaaa\".\n\nSergey does not like such behavior, so he wants to write a program to format the words written by Stepan. This program must combine all cons... | {
"inputs": [
"13\npobeeeedaaaaa\n",
"22\niiiimpleeemeentatiioon\n",
"18\naeiouyaaeeiioouuyy\n",
"24\naaaoooiiiuuuyyyeeeggghhh\n",
"36\naeiouyaaeeiioouuyyaaaeeeiiiooouuuyyy\n",
"100\noiyufyyyioueoudosizoryuoedatenougiuaeuouuyoiimaeigeeycewuooyovacoiyuaygfuuaiaeuahuieeafxsciylaebeufi\n",
"2... | code | code | {
"domain": "code",
"data_source": "apps",
"src_index": 7752
} |
[
{
"role": "user",
"content": "Petya loves volleyball very much. One day he was running late for a volleyball match. Petya hasn't bought his own car yet, that's why he had to take a taxi. The city has n junctions, some of which are connected by two-way roads. The length of each road is defined by some positi... | {"inputs": ["4 4\n1 3\n1 2 3\n1 4 1\n2 4 1\n2 3 5\n2 7\n7 2\n1 2\n7 7\n", "5 7\n1 3\n1 2 1\n1 3 3\n1 5 1\n1 4 2\n5 4 3\n3 5 2\n2 3 8\n2 7\n10 3\n4 7\n2 1\n1 1\n", "3 2\n3 3\n1 2 2\n1 3 3\n2 7\n2 7\n3 7\n", "7 15\n5 5\n3 4 6\n7 4 3\n7 2 8\n2 5 2\n7 2 8\n5 2 9\n3 1 7\n1 2 4\n7 1 8\n7 5 7\n2 4 2\n4 3 9\n7 4 2\n5 4 8\n7 2 ... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 21008
} |
[
{
"role": "user",
"content": "Evaluate the surface integral \\( \\iint_S \\vec{F} \\cdot d\\vec{S} \\), where \\( \\vec{F} = y\\hat{i} + x\\hat{j} + zy\\hat{k} \\) and \\( S \\) is the part of the surface \\( z = x^2 + y^2 \\) that lies above \\( z = 1 \\). Assume \\( S \\) has an upwards orientation.\nPlea... | 0 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 9012
} |
[
{
"role": "user",
"content": "Let $x_0, \\ldots , x_{n-1}$ denote $n$ boolean variables (i.e., variables taking only values $0$ and $1$). A binary decision diagram (BDD) over these variables is a diagrammatic representation of a boolean function $f(x_0, \\ldots , x_{n-1})$ as inputs.\n\nA BDD is a rooted bi... | {"inputs": ["2\n1 1 0 1\n", "2\n0 0 0 0\n", "3\n1 0 1 0 1 1 1 0\n"], "outputs": ["5\n", "1\n", "7\n"]} | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 20807
} |
[
{
"role": "user",
"content": "Give practical advice about a narrow staircase.\n\nFollow ALL of these requirements exactly:\n- End your answer with \"-- done --\".\n- Answer in exactly 3 sentences.\n- Begin by repeating this exactly: \"Give practical advice about a narrow staircase.\""
}
] | [{"type": "ends_with", "value": "-- done --"}, {"type": "sentence_count", "n": 3}, {"type": "repeat_first", "value": "Give practical advice about a narrow staircase."}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 6838
} |
[
{
"role": "user",
"content": "Summarise what matters most about an empty theatre.\n\nFollow ALL of these requirements exactly:\n- Begin your answer with \"Answer:\"."
}
] | [{"type": "starts_with", "value": "Answer:"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 6725
} |
[
{
"role": "user",
"content": "Krishnakant is standing at $(0,0)$ in the Cartesian plane. He wants to go to the point $(x,y)$ in the same plane using only horizontal and vertical moves of $1$ unit. There are many ways of doing this, and he is writing down all such ways. Each way comprises of few ${H}$ moves ... | {"inputs": ["5\n2 2 0\n3 3 2\n4 4 2\n4 4 3\n3 3 1\n", "1\n3 3 1\n", "1\n10 10 10\n", "1\n10 10 9\n", "1\n10 10 8\n", "1\n10 10 11\n", "1\n10 10 12\n"], "outputs": ["HHVV\nHHVVHV\nHHHVVHVV\nHHHVVVHV\nHHVHVV", "HHVHVV", "HHHHHHHHHVVVVVVVVVVH", "HHHHHHHHHVVVVVVVVVHV", "HHHHHHHHHVVVVVVVVHVV", "HHHHHHHHVHHVVVVVVVVV", "HHHHH... | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 5078
} |
[
{
"role": "user",
"content": "Is it true that there are only five bounded connected non-selfintersecting polyhedra with identical regular-polygon faces and congruent vertices, namely the Platonic solids?\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 22198
} |
[
{
"role": "user",
"content": "In Berland the opposition is going to arrange mass walking on the boulevard. The boulevard consists of n tiles that are lain in a row and are numbered from 1 to n from right to left. The opposition should start walking on the tile number 1 and the finish on the tile number n. D... | {"inputs": ["5\n10 2 8 3 5\n", "4\n10 3 5 10\n", "50\n14 4 20 37 50 46 19 20 25 47 10 6 34 12 41 47 9 22 28 41 34 47 40 12 42 9 4 15 15 27 8 38 9 4 17 8 13 47 7 9 38 30 48 50 7 41 34 23 11 16\n", "1\n1\n", "10\n5 17 8 1 10 20 9 18 12 20\n", "25\n220 93 216 467 134 408 132 220 292 11 363 404 282 253 141 313 310 356 214 ... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 8319
} |
[
{
"role": "user",
"content": "Find the flux of the vector field \\( \\mathbf{F} = (2x-xy, -y, yz) \\) out of the region \\( W \\), where \\( W \\) is the 3D region under the graph of \\( f(x,y) = \\exp(x^2+y^2) \\) over the region in the plane defined by \\( 1 \\leq x^2 + y^2 \\leq 2 \\). Verify your answer... | \pi (e^2 - e) | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 17176
} |
[
{
"role": "user",
"content": "Chef has with him an array A of length N. In one move, he can delete any element from A.\n\nFind the minimum number of deletions Chef must make so that the following condition holds:\nLet B denote the resulting array, and M be the length of B.\nThen, B_{i} \\oplus B_{j} ≤ 1 for... | {"inputs": ["1\n5\n4 5 5 4 4\n", "1\n6\n1 2 3 4 5 6\n", "1\n7\n3 4 3 5 4 5 4\n", "1\n10\n2 2 2 2 2 4 4 4 4 4\n", "1\n10\n5 6 5 5 6 5 6 7 8 9\n", "1\n10\n3 4 5 6 7 8 9 10 11 12\n"], "outputs": ["0", "4", "2", "5", "6", "8"]} | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 17141
} |
[
{
"role": "user",
"content": "Student Valera is an undergraduate student at the University. His end of term exams are approaching and he is to pass exactly n exams. Valera is a smart guy, so he will be able to pass any exam he takes on his first try. Besides, he can take several exams on one day, and in any... | {"inputs": ["3\n5 2\n3 1\n4 2\n", "3\n6 1\n5 2\n4 3\n", "1\n1000000000 999999999\n", "5\n4 3\n4 2\n4 1\n4 1\n4 1\n", "6\n12 11\n10 9\n8 7\n6 5\n4 3\n2 1\n", "2\n3 1\n3 2\n", "3\n3 2\n4 1\n100 10\n", "2\n4 2\n4 1\n", "4\n7 1\n7 3\n8 2\n9 8\n", "3\n3 2\n4 1\n10 5\n", "2\n5 2\n5 1\n", "5\n6 5\n6 4\n6 3\n6 2\n6 1\n", "3\n5... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 400
} |
[
{
"role": "user",
"content": "Given a sequence of integers a_1, ..., a_{n} and q queries x_1, ..., x_{q} on it. For each query x_{i} you have to count the number of pairs (l, r) such that 1 ≤ l ≤ r ≤ n and gcd(a_{l}, a_{l} + 1, ..., a_{r}) = x_{i}.\n\n$\\operatorname{gcd}(v_{1}, v_{2}, \\ldots, v_{n})$ is a... | {
"inputs": [
"3\n2 6 3\n5\n1\n2\n3\n4\n6\n",
"7\n10 20 3 15 1000 60 16\n10\n1\n2\n3\n4\n5\n6\n10\n20\n60\n1000\n",
"10\n2 2 4 3 2 4 4 2 4 2\n104\n3\n3\n1\n4\n1\n1\n4\n1\n1\n3\n1\n1\n4\n1\n1\n1\n4\n3\n1\n1\n4\n1\n1\n1\n1\n1\n4\n1\n1\n1\n4\n1\n1\n4\n1\n1\n1\n1\n1\n4\n4\n1\n3\n1\n4\n1\n1\n1\n4\n1\n2\n4\n1\n... | code | code | {
"domain": "code",
"data_source": "apps",
"src_index": 4815
} |
[
{
"role": "user",
"content": "Let \\( f(x) = a_{5} x^{5} + a_{4} x^{4} + \\cdots + a_{1} x + a_{0} \\), \\( g(x) = b_{3} x^{3} + b_{2} x^{2} + b_{1} x + b_{0} \\), and \\( h(x) = c_{2} x^{2} + c_{1} x + c_{0} \\) be polynomials with integer coefficients such that the absolute values of the coefficients of \... | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 52769
} |
[
{
"role": "user",
"content": "Explain why someone might find a missed connection memorable.\n\nFollow ALL of these requirements exactly:\n- Use at most 120 words.\n- Include at least 1 placeholders in square brackets, like [name]."
}
] | [{"type": "word_count_max", "n": 120}, {"type": "placeholder_count", "n": 1}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 6014
} |
[
{
"role": "user",
"content": "Evaluate the integral \\(\\int_{-\\infty}^{\\infty}\\frac{x^3}{(x^2+4)(x^2+1)}\\;dx\\) using complex analysis and the residue theorem.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 0 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 24790
} |
[
{
"role": "user",
"content": "Give practical advice about an empty picture frame.\n\nFollow ALL of these requirements exactly:\n- Use at most 120 words.\n- Do not use the letter 'a' anywhere.\n- Highlight at least 2 sections using **double asterisks**."
}
] | [{"type": "word_count_max", "n": 120}, {"type": "forbidden_chars", "values": ["a"]}, {"type": "highlight_count", "n": 2}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 4878
} |
[
{
"role": "user",
"content": "Find all values of the constant $k$ for which the function $u(x,y) = x^{3} - kxy^{2} + 12xy - 12x$ is the real part of a holomorphic function.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 3 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 2805
} |
[
{
"role": "user",
"content": "Fennec and Snuke are playing a board game.\n\nOn the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an ad... | {"inputs": ["4\n1 4\n4 2\n2 3", "7\n3 6\n1 2\n3 1\n7 4\n5 7\n1 4", "4\n1 4\n4 3\n2 3", "7\n3 6\n2 2\n3 1\n7 4\n5 7\n1 4", "7\n3 6\n2 2\n3 1\n7 4\n4 7\n1 4", "7\n3 6\n1 2\n3 2\n7 4\n5 7\n1 4", "7\n3 6\n2 2\n3 1\n5 4\n4 7\n1 4", "4\n1 2\n4 2\n2 3", "4\n1 4\n4 3\n2 1", "7\n3 6\n1 2\n3 1\n7 4\n5 7\n2 4", "4\n1 4\n4 3\n2 2"... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 15561
} |
[
{
"role": "user",
"content": "Chef has an array A of length N.\n\nLet f(i) denote the sum A_{1} + A_{2} + \\dots + A_{i} \\, and let g(i) denote the sum A_{i} + A_{i + 1} + \\dots + A_{N}. \n\nChef creates another array B of length N such that B_{i} = f(i) + g(i) for all 1 ≤ i ≤ N.\n\nNow, Chef has lost the... | {"inputs": ["1\n2\n5 6\n", "1\n3\n6 7 8\n", "1\n4\n10 12 14 16\n", "1\n5\n11 13 15 17 19\n", "1\n2\n100000 100000\n", "1\n2\n2 2\n", "1\n3\n5 5 5\n", "1\n2\n20000000000 20000000000\n", "1\n3\n10000000000 10000000000 10000000000\n"], "outputs": ["2 3", "1 2 3", "0 2 4 6", "-1 1 3 5 7", "33334 33334", "1 1", "2 2 2", "66... | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 18487
} |
[
{
"role": "user",
"content": "Hint\n\nIn solving this problem, the following may be referred to. Shows how to convert an integer value to a string. Assign value as a string to str.\n\nFor C\n\n\ninclude <stdio.h>\n\nint main () {\nint value = 123; // Convert this value to a string\nchar str [6]; // This var... | {"inputs": ["5 30\n13 51 32 9 2 1 10 2 5 10", "1 10\n1 2 3 4 7 6 7 8 9 10", "5 100\n101 101 101 101 101 101 101 101 100 101", "5 10\n8 4 5 3 5 6 9 10 11 2", "5 35\n13 51 32 14 2 1 10 2 5 10", "7 35\n13 51 32 14 2 1 10 2 5 10", "7 35\n13 51 1 14 2 1 10 2 5 10", "5 30\n25 51 32 9 2 1 10 2 5 18", "5 100\n101 101 101 101 0... | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 10112
} |
[
{
"role": "user",
"content": "If \\(x = \\sqrt{2} + \\sqrt{3} + \\sqrt{6}\\) is a root of the polynomial \\(x^4 + ax^3 + bx^2 + cx + d = 0\\), find the value of \\(|a+b+c+d|\\).\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 93 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 10399
} |
[
{
"role": "user",
"content": "Describe an old wristwatch without using technical jargon.\n\nFollow ALL of these requirements exactly:\n- Answer in exactly 5 sentences.\n- End your answer with \"-- done --\"."
}
] | [{"type": "sentence_count", "n": 5}, {"type": "ends_with", "value": "-- done --"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 3919
} |
[
{
"role": "user",
"content": "Explain how magnets attract to someone who has never encountered it.\n\nFollow ALL of these requirements exactly:\n- Answer as exactly 3 bullet points, each starting with '- '."
}
] | [{"type": "bullet_count", "n": 3}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 3796
} |
[
{
"role": "user",
"content": "Describe an empty theatre without using technical jargon.\n\nFollow ALL of these requirements exactly:\n- Write your entire answer in capital letters."
}
] | [{"type": "all_caps"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 4193
} |
[
{
"role": "user",
"content": "Let $A$ be an $n \\times n$ real matrix such that all its conjugates (matrices similar to $A$ over $\\mathbb{R}$) have zero diagonal entries. Determine whether it is necessarily true that $A=0$. Provide a justification for your answer.\nPlease reason step by step, and put your ... | A = 0 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 28278
} |
[
{
"role": "user",
"content": "Title: Circle Line\n\nTime Limit: None seconds\n\nMemory Limit: None megabytes\n\nProblem Description:\nThe circle line of the Berland subway has *n* stations. We know the distances between all pairs of neighboring stations:\n- *d*1 is the distance between the 1-st and the 2-n... | {"inputs": ["4\n2 3 4 9\n1 3", "4\n5 8 2 100\n4 1", "3\n1 1 1\n3 1", "3\n31 41 59\n1 1", "5\n16 13 10 30 15\n4 2", "6\n89 82 87 32 67 33\n4 4", "7\n2 3 17 10 2 2 2\n4 2", "3\n4 37 33\n3 3", "8\n87 40 96 7 86 86 72 97\n6 8", "10\n91 94 75 99 100 91 79 86 79 92\n2 8", "19\n1 1 1 1 2 1 1 1 1 1 2 1 3 2 2 1 1 1 2\n7 7", "34... | code | code | {
"domain": "code",
"data_source": "codeforces",
"src_index": 22165
} |
[
{
"role": "user",
"content": "Give practical advice about how compasses point north.\n\nFollow ALL of these requirements exactly:\n- Use at most 90 words.\n- Do not use any commas.\n- Use at least 80 words."
}
] | [{"type": "word_count_max", "n": 90}, {"type": "no_commas"}, {"type": "word_count_min", "n": 80}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 3362
} |
[
{
"role": "user",
"content": "Write a brief reflection on the last bus home.\n\nFollow ALL of these requirements exactly:\n- Do not use the letter 'z' anywhere.\n- Answer as exactly 2 bullet points, each starting with '- '.\n- Answer as exactly 4 numbered items, like '1. '."
}
] | [{"type": "forbidden_chars", "values": ["z"]}, {"type": "bullet_count", "n": 2}, {"type": "numbered_count", "n": 4}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 5411
} |
[
{
"role": "user",
"content": "If $a_n$ converges in probability to $0$ but $b_n$ does not have a probability limit, does $a_n + b_n$ converge in probability to $0$?\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | No | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 2786
} |
[
{
"role": "user",
"content": "Given a set of $n$ intervals, find the size of its largest possible subset of intervals such that no three intervals in the subset share a common point.\n\nInput Format\n\nThe first line contains an integer, $\\boldsymbol{\\mathrm{~S~}}$, denoting the number of interval sets yo... | {"inputs": [" 1\n3\n1 2\n2 3\n3 4\n"], "outputs": ["3"]} | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 1595
} |
[
{
"role": "user",
"content": "Explain why someone might find an interrupted phone call memorable.\n\nFollow ALL of these requirements exactly:\n- Do not use any commas.\n- Begin your answer with \"In short:\"."
}
] | [{"type": "no_commas"}, {"type": "starts_with", "value": "In short:"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1163
} |
[
{
"role": "user",
"content": "Explain why someone might find a city at night memorable.\n\nFollow ALL of these requirements exactly:\n- Highlight at least 3 sections using **double asterisks**.\n- Do not use any commas."
}
] | [{"type": "highlight_count", "n": 3}, {"type": "no_commas"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 7206
} |
[
{
"role": "user",
"content": "Explain why someone might find why milk curdles memorable.\n\nFollow ALL of these requirements exactly:\n- Write your entire answer in lowercase letters only.\n- Include at least 1 placeholders in square brackets, like [name]."
}
] | [{"type": "all_lowercase"}, {"type": "placeholder_count", "n": 1}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1553
} |
[
{
"role": "user",
"content": "Eleven wants to choose a new name for herself. As a bunch of geeks, her friends suggested an algorithm to choose a name for her. Eleven wants her name to have exactly n characters. \n\n<image>\n\nHer friend suggested that her name should only consist of uppercase and lowercase ... | {"inputs": ["8\n", "15\n", "381\n", "1000\n", "5\n", "781\n", "999\n", "805\n", "3\n", "61\n", "256\n", "512\n", "1\n", "17\n", "2\n", "933\n", "85\n", "49\n", "431\n", "9\n", "859\n", "339\n", "6\n", "7\n", "254\n", "78\n", "898\n", "136\n", "47\n", "4\n", "27\n", "485\n", "33\n", "681\n", "97\n", "10\n", "22\n", "141... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 8440
} |
[
{
"role": "user",
"content": "Little Petya likes to play a lot. Most of all he likes to play a game «Holes». This is a game for one person with following rules:\n\nThere are N holes located in a single row and numbered from left to right with numbers from 1 to N. Each hole has it's own power (hole number i ... | {"inputs": ["10 10\n5 1 2 4 1 7 3 8 10 8\n0 5 6\n1 8\n1 1\n0 10 3\n1 5\n1 3\n1 2\n0 6 1\n1 9\n1 1\n", "10 10\n5 1 2 8 1 7 3 8 10 8\n0 5 6\n1 8\n1 1\n0 10 3\n1 5\n1 3\n1 2\n0 6 1\n1 9\n1 1\n", "8 5\n1 1 1 1 1 1 8 2\n1 1\n0 1 3\n1 1\n0 3 4\n1 2\n", "8 5\n1 1 1 1 1 2 11 2\n1 1\n0 1 3\n1 1\n0 3 4\n1 2\n", "8 5\n1 1 1 1 1 2... | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 16962
} |
[
{
"role": "user",
"content": "Evaluate the limit \\( \\lim_{x \\rightarrow 1^{-} } \\frac{e^{1/(x^2 -1)}}{x-1} \\).\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 0 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 35920
} |
[
{
"role": "user",
"content": "Given that \\( 3f(x) = 3x^4 + x^3 + 3x^2 \\), evaluate the limit \\( \\lim_{a \\to \\infty} \\int_{2a}^{8a} \\frac{1}{(f^{-1}(x))^2 + (f^{-1}(x))^4} \\, dx = \\ln(n) \\). Find the value of \\( n \\).\nPlease reason step by step, and put your final answer within \\boxed{}."
}
... | 4 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 885
} |
[
{
"role": "user",
"content": "Determine whether there exists an unbounded sequence \\( y_n \\) for \\( n \\geq 0 \\) such that \\( y_{n+m} \\geq \\frac{y_n + y_m}{2} \\) for all \\( n, m \\geq 0 \\).\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 36718
} |
[
{
"role": "user",
"content": "Describe an argument about directions as it would appear to a first-time visitor.\n\nFollow ALL of these requirements exactly:\n- End your answer with \"THE END\".\n- Answer as exactly 3 numbered items, like '1. '."
}
] | [{"type": "ends_with", "value": "THE END"}, {"type": "numbered_count", "n": 3}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 4285
} |
[
{
"role": "user",
"content": "For a field $K$, determine if there exists a division ring $D$ containing $K$ as a central subring such that the dimension of $D$ over $K$ is less than the cardinality of $K$. Provide a justification for your answer.\nPlease reason step by step, and put your final answer within... | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 48198
} |
[
{
"role": "user",
"content": "You are given a permutation of 1,2,...,N: p_1,p_2,...,p_N. Determine if the state where p_i=i for every i can be reached by performing the following operation any number of times:\n\n* Choose three elements p_{i-1},p_{i},p_{i+1} (2\\leq i\\leq N-1) such that p_{i-1}>p_{i}>p_{i+... | {"inputs": ["6\n5\n3\n4\n1\n2\n6", "5\n5\n2\n1\n4\n3", "4\n3\n2\n4\n1", "7\n3\n2\n1\n6\n5\n4\n7", "6\n5\n3\n8\n1\n2\n6", "4\n3\n2\n3\n1", "6\n5\n3\n8\n1\n2\n3", "4\n3\n2\n2\n1", "6\n4\n3\n8\n1\n2\n3", "4\n3\n1\n2\n1", "4\n6\n1\n2\n1", "4\n10\n1\n2\n1", "4\n10\n1\n2\n2", "4\n10\n1\n2\n4", "4\n8\n1\n2\n4", "6\n5\n3\n4\n1... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 12210
} |
[
{
"role": "user",
"content": "The Resistance is trying to take control over all planets in a particular solar system. This solar system is shaped like a tree. More precisely, some planets are connected by bidirectional hyperspace tunnels in such a way that there is a path between every pair of the planets, ... | {
"inputs": [
"5\n4 1\n4 2\n1 3\n1 5\n",
"4\n1 2\n4 3\n1 4\n",
"10\n4 3\n2 6\n10 1\n5 7\n5 8\n10 6\n5 9\n9 3\n2 9\n"
],
"outputs": [
"3\n",
"2\n",
"4\n"
]
} | code | code | {
"domain": "code",
"data_source": "apps",
"src_index": 20924
} |
[
{
"role": "user",
"content": "Explain why someone might find a lost glove in winter memorable.\n\nFollow ALL of these requirements exactly:\n- Include at least 3 placeholders in square brackets, like [name]."
}
] | [{"type": "placeholder_count", "n": 3}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 3665
} |
[
{
"role": "user",
"content": "Consider a non-empty set $S$ with a binary operation $*$, forming a magma $(S, *)$. Given that $a*(b*c) = (c*a)*b$ for all $a, b, c \\in S$, determine if it is possible for $(S, *)$ to have neither a left identity nor a right identity.\nPlease reason step by step, and put your ... | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 50873
} |
[
{
"role": "user",
"content": "Give practical advice about the sound of a metronome.\n\nFollow ALL of these requirements exactly:\n- Do not use the letter 'e' anywhere.\n- Write your entire answer in lowercase letters only.\n- Answer as exactly 2 bullet points, each starting with '- '."
}
] | [{"type": "forbidden_chars", "values": ["e"]}, {"type": "all_lowercase"}, {"type": "bullet_count", "n": 2}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1856
} |
[
{
"role": "user",
"content": "Read problems statements in Mandarin Chinese and Russian. \n\nTanu has got interested in signs and gestures that we use for communication. One such gesture is the head-bob.\nWhen we want to signal \"Yes\" to someone, we move the head up-and-down. For \"No\", the head is moved ... | {"inputs": ["3\n5\nNNNYY\n6\nNNINNI\n4\nNNNN"], "outputs": ["NOT INDIAN\nINDIAN\nNOT SURE"]} | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 19340
} |
[
{
"role": "user",
"content": "Explain the smell of a library to someone who has never encountered it.\n\nFollow ALL of these requirements exactly:\n- Include at least 1 placeholders in square brackets, like [name]."
}
] | [{"type": "placeholder_count", "n": 1}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1760
} |
[
{
"role": "user",
"content": "Summarise what matters most about a narrow staircase.\n\nFollow ALL of these requirements exactly:\n- End your answer with \"THE END\".\n- Include at least 1 placeholders in square brackets, like [name]."
}
] | [{"type": "ends_with", "value": "THE END"}, {"type": "placeholder_count", "n": 1}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 4753
} |
[
{
"role": "user",
"content": "Give practical advice about an empty swimming pool.\n\nFollow ALL of these requirements exactly:\n- Write your entire answer in lowercase letters only.\n- Use at least 80 words."
}
] | [{"type": "all_lowercase"}, {"type": "word_count_min", "n": 80}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 143
} |
[
{
"role": "user",
"content": "Given positive integers \\(a\\), \\(b\\) \\((a \\leq b)\\), a sequence \\(\\{ f_{n} \\}\\) satisfies:\n\\[ f_{1} = a, \\, f_{2} = b, \\, f_{n+2} = f_{n+1} + f_{n} \\text{ for } n = 1, 2, \\ldots \\]\n\nIf for any positive integer \\(n\\), it holds that \n\\[ \\left( \\sum_{k=1}... | 2 + \sqrt{5} | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 53205
} |
[
{
"role": "user",
"content": "Given two matrices $M_1, M_2 \\in \\mathbb{R}^{k \\times l}$, and two orthogonal matrices $U \\in \\mathbb{R}^{k \\times k}$, $V \\in \\mathbb{R}^{l \\times l}$ such that $M_2 = UM_1V$. If $\\text{tr}(M_1) = \\text{tr}(M_2)$, can we conclude that $M_1 = M_2$?\nPlease reason ste... | No | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 47924
} |
[
{
"role": "user",
"content": "Write a short description of the taste of cold water.\n\nFollow ALL of these requirements exactly:\n- Reply with valid JSON and nothing else.\n- Your answer must contain the word \"orange\"."
}
] | [{"type": "valid_json"}, {"type": "must_include", "values": ["orange"]}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 6861
} |
[
{
"role": "user",
"content": "Summarise what matters most about the sound of a violin.\n\nFollow ALL of these requirements exactly:\n- End your answer with \"THE END\".\n- Write your entire answer in capital letters."
}
] | [{"type": "ends_with", "value": "THE END"}, {"type": "all_caps"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 1376
} |
[
{
"role": "user",
"content": "Give practical advice about how sundials tell time.\n\nFollow ALL of these requirements exactly:\n- Answer as exactly 2 bullet points, each starting with '- '."
}
] | [{"type": "bullet_count", "n": 2}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 2177
} |
[
{
"role": "user",
"content": "Write a short description of an empty swimming pool.\n\nFollow ALL of these requirements exactly:\n- Do not use the letter 'a' anywhere.\n- Reply with valid JSON and nothing else."
}
] | [{"type": "forbidden_chars", "values": ["a"]}, {"type": "valid_json"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 4059
} |
[
{
"role": "user",
"content": "Find the number of ordered pairs \\((a, b)\\) that satisfy the equation \\((a+b \\mathrm{i})^{6}=a-b \\mathrm{i}\\), where \\(a, b \\in \\mathbf{R}\\) and \\(\\mathrm{i}^{2}=-1\\).\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 8 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 56093
} |
[
{
"role": "user",
"content": "Polycarpus participates in a competition for hacking into a new secure messenger. He's almost won.\n\nHaving carefully studied the interaction protocol, Polycarpus came to the conclusion that the secret key can be obtained if he properly cuts the public key of the application i... | {"inputs": ["116401024\n97 1024\n", "284254589153928171911281811000\n1009 1000\n", "120\n12 1\n", "604\n6 4\n", "2108\n7 8\n", "7208\n10 1\n", "97502821\n25 91\n", "803405634\n309 313\n", "15203400\n38 129\n", "8552104774\n973 76\n", "2368009434\n320 106\n", "425392502895812\n4363 2452\n", "142222201649130\n4854 7853\n... | code | code | {
"domain": "code",
"data_source": "taco",
"src_index": 3659
} |
[
{
"role": "user",
"content": "Give practical advice about a missed connection.\n\nFollow ALL of these requirements exactly:\n- Reply with valid JSON and nothing else.\n- Your answer must not contain the word \"harbour\", the word \"lantern\".\n- Write your entire answer in capital letters."
}
] | [{"type": "valid_json"}, {"type": "must_exclude", "values": ["harbour", "lantern"]}, {"type": "all_caps"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 2551
} |
[
{
"role": "user",
"content": "Determine whether the following identity is true for an indeterminate $x$ and a non-negative integer $n$:\n\\[ x\\prod_{k=1}^n(k^2-x^2)=\\frac1{4^n}\\sum_{m=0}^n\\binom{n-x}m\\binom{n+x}{n-m}(x+2m-n)^{2n+1}. \\]\nPlease reason step by step, and put your final answer within \\bo... | True | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 19637
} |
[
{
"role": "user",
"content": "Explain a misplaced key to someone who has never encountered it.\n\nFollow ALL of these requirements exactly:\n- Your answer must not contain the word \"orange\", the word \"market\".\n- Use at most 90 words.\n- Begin your answer with \"Answer:\"."
}
] | [{"type": "must_exclude", "values": ["orange", "market"]}, {"type": "word_count_max", "n": 90}, {"type": "starts_with", "value": "Answer:"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 7126
} |
[
{
"role": "user",
"content": "Evaluate the second-order partial derivative \\( \\frac{\\partial^2 f}{\\partial x \\partial y}(0,0) \\) for the function \\( f(x,y)= \\begin{cases} \\frac{xy(x^2-y^2)}{x^2+y^2} &\\text {if }(x,y) \\neq (0,0) \\\\ 0 & \\text{otherwise}\\end{cases} \\).\nPlease reason step by st... | 1 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 25372
} |
[
{
"role": "user",
"content": "Determine the functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that every point is a local maximum.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | f(x) = c | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 46224
} |
[
{
"role": "user",
"content": "Given a rational polyhedron $P=\\{x|Ax\\le b\\}$ where $A$ is an $m \\times n$ matrix with rational entries and $b$ is a rational vector, determine if every supporting hyperplane can be defined using an integral vector $c$ and an integer $d$. Specifically, can every face $F$ of... | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 39698
} |
[
{
"role": "user",
"content": "Explain how wells draw water to someone who has never encountered it.\n\nFollow ALL of these requirements exactly:\n- Begin your answer with \"Here is my reply:\"."
}
] | [{"type": "starts_with", "value": "Here is my reply:"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 253
} |
[
{
"role": "user",
"content": "Find an example of a constructible angle that cannot be quintsected using an unmarked straightedge and compass.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | 72^\circ | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 2397
} |
[
{
"role": "user",
"content": "Kitahara Haruki has bought n apples for Touma Kazusa and Ogiso Setsuna. Now he wants to divide all the apples between the friends.\n\nEach apple weights 100 grams or 200 grams. Of course Kitahara Haruki doesn't want to offend any of his friend. Therefore the total weight of the... | {"inputs": ["4\n100 100 100 200\n", "3\n100 200 100\n", "9\n100 100 100 200 100 100 200 100 200\n", "3\n100 100 100\n", "7\n200 200 200 100 200 200 200\n", "100\n100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 10... | code | code | {
"domain": "code",
"data_source": "codecontests",
"src_index": 18945
} |
[
{
"role": "user",
"content": "Find a condition on the constant $c$ such that the inequality \\( \\frac{1 - e^{-st}}{st} - \\frac{1}{st+c} > 0 \\) holds for all positive real numbers $s$ and $t$.\nPlease reason step by step, and put your final answer within \\boxed{}."
}
] | c \geq 1 | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 44818
} |
[
{
"role": "user",
"content": "Explain how sponges absorb to someone who has never encountered it.\n\nFollow ALL of these requirements exactly:\n- Do not use any commas.\n- Write your entire answer in capital letters."
}
] | [{"type": "no_commas"}, {"type": "all_caps"}] | ifeval | ifeval | {
"domain": "ifeval",
"data_source": "synthetic-ifeval-v1",
"src_index": 7793
} |
[
{
"role": "user",
"content": "Let $K$ be a finite extension of $\\mathbb{Q}_p$, and $\\mathcal{O}$ the ring of integers of $K$. Let $\\mathfrak{p}$ be the maximal ideal of $\\mathcal{O}$. Is the quotient ring $\\mathcal{O}/\\mathfrak{p}^n$ finite for all $n > 0$?\nPlease reason step by step, and put your fi... | Yes | math | math | {
"domain": "math",
"data_source": "DeepMath-103K",
"src_index": 14833
} |
[
{
"role": "user",
"content": "Title: Xenia and Tree\n\nTime Limit: None seconds\n\nMemory Limit: None megabytes\n\nProblem Description:\nXenia the programmer has a tree consisting of *n* nodes. We will consider the tree nodes indexed from 1 to *n*. We will also consider the first node to be initially painte... | {"inputs": ["5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 5\n1 2\n2 5"], "outputs": ["0\n3\n2"]} | code | code | {
"domain": "code",
"data_source": "codeforces",
"src_index": 12696
} |
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