context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 9
values | metadata dict | model_outputs stringlengths 1 123k |
|---|---|---|---|---|---|---|
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The conductance of a $0.0015 \\mathrm{M}$ aqueous solution of a weak monobasic acid was determined by using a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 80 | JEEBench | {
"expected_answer": "6",
"problem_id": "27",
"reference_solution": null,
"subject": "chem",
"type": "Integer"
} | <think>
Okay, so I need to find the value of Z in the limiting molar conductivity (Λ_m^o) of a weak monobasic acid. The given data is:
- The solution is 0.0015 M (which is 1.5 × 10^-3 M)
- The conductance (G) of the solution is 5 × 10^-7 S
- The pH of the solution is 4
- The distance between the electrodes (d) is 120... |
[
{
"content": "Problem: A number is selected at random from 1 through 100, inclusive. What is the probability that the number is a multiple of 3?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 266 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the probability that a number selected at random from 1 through 100 is a multiple of 3. Hmm, let's start by recalling what probability means. The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the total number o... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: The best available evidence for an association between amount of sugars and risk of dental caries comes from which type of study design?\n \nOptions:... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 312 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the best type of study design for assessing the association between sugar consumption and dental caries risk, let's consider the characteristics of each study type listed.
1. **Cohort Study (A)**: This involves following a group over time, examining those exposed and not exposed to a factor. It can establ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 325 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have students lined up, each with a topic of interest, and we want to minimize the number of neighboring pairs with the same topic. The way to do this is by swapping students at positions i and n-i+1 any number of times. Hmm, interesting. Let me try to break thi... |
[
{
"content": "Problem: Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by $20\\%$ on every pair of shoes. Carlos also knew that he had to pay a $7.5\\%$ sales tax on the discounted price. He had $$43$ dollars. What is the original (before discount) price of th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 30 | AMC23 | {
"expected_answer": "50",
"problem_id": "36",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let me try to figure out this problem. So, Carlos is going to the sports store to buy running shoes. The shoes are on sale with a 20% discount, and there's a 7.5% sales tax on the discounted price. Carlos has $43 to spend. We need to find the original price of the most expensive shoes he can afford. Hmm, ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A projectile is thrown from a point $\\mathrm{O}$ on the groun... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 314 | JEEBench | {
"expected_answer": "7.5",
"problem_id": "6",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Alright, let me try to figure out this problem step by step. So, we have a projectile launched from point O on the ground at an angle of 45 degrees from the vertical with a speed of 5√2 m/s. At the highest point of its trajectory, the projectile splits into two equal parts. One part falls vertically down to the... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N intervals of real numbers. The i-th (1 \\leq i \\leq N) interval is [l_i, r_i]. Find the number of pai... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 456 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to find the number of pairs of intervals (i, j) where i < j and the intervals [l_i, r_i] and [l_j, r_j] intersect.
The key observation here is that two intervals [a, b] and [c, d] intersect if and only if a < d and c < b. Alternatively, if the maximum of the left endpoints is less than ... |
[
{
"content": "Problem: Flora the frog starts at 0 on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance $m$ with probability $\\frac{1}{2^m}$.\nWhat is the probability that Flora will eventually land at 10? Write th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 7 | AMC23 | {
"expected_answer": "3",
"problem_id": "8",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the probability that Flora the frog will eventually land at 10 on the number line. Each jump she makes is a positive integer distance m with probability 1/(2^m). Hmm, let's see.
First, I remember that for a problem like this, where each step has a certain probability, we might ne... |
[
{
"content": "Problem: Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take turns with Alice going first. On each turn, the player removes either $1$ token or $4$ tokens from the stack. Whoever removes the last token wins. Find the number of positive integers $n... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 9,
"temperature": 0.7
} | 9 | 17 | AIME24 | {
"expected_answer": "809",
"problem_id": "aime24-17",
"reference_solution": "Let's first try some experimentation. Alice obviously wins if there is one coin. She will just take it and win. If there are 2 remaining, then Alice will take one and then Bob will take one, so Bob wins. If there are $3$ , Alice will t... | <think>
Okay, so I need to figure out how many positive integers n ≤ 2024 allow Bob to have a winning strategy regardless of what Alice does. The game is where they take turns removing 1 or 4 tokens, and the player who takes the last token wins. Let me start by understanding the problem step by step.
First, let's thin... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 425 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a tree with n vertices, and we have to find the minimum expected number of steps for a robot to reach vertex 1, given that we can spend up to p coins to control its movement. The problem also mentions that we need to answer q queries, each with a different v a... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 331 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether a permutation exists for a given string `s` where certain positions require subarrays to also form permutations. Let me try to break down the problem step by step.
First, let's parse the problem statement again to make sure I understand all the details. We have a string `s... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 32 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where given an integer n and some sets V_i, I have to find all subsets S of {0,1,...,n-1} such that for every non-empty subset T of {0,1,...,n-1}, the size of the intersection of S and T is in V_{f(T)}. Then, I need to output the number of such subsets and their binary enco... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: How does pure capitalism determine what goods are to be produced?\nOptions: A. Goods are determined by the quantity of raw materials, B. The types an... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 421 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how pure capitalism determines what goods are produced. Let me start by recalling what pure capitalism is. From what I remember, in a purely capitalist economy, the means of production are privately owned, and the government doesn't interfere with business decisions. The idea is th... |
[
{
"content": "Problem: Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and\n \\[a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 10 | AIME24 | {
"expected_answer": "601",
"problem_id": "aime24-10",
"reference_solution": "$ab(a+b)+bc(b+c)+ac(a+c)=300(ab+bc+ac)-3abc=6000000, 100(ab+bc+ac)-abc=2000000$ Note that \n $(100-a)(100-b)(100-c)=1000000-10000(a+b+c)+100(ab+bc+ac)-abc=0$ . Thus, $a/b/c=100$ . There are $201$ cases for each but we need to subtrac... | <think>
Okay, so I need to find the number of triples of nonnegative integers (a, b, c) such that a + b + c = 300 and the sum of all products of two variables and the third one is equal to 6,000,000. Let me try to parse this step by step.
First, the equation a + b + c = 300 is straightforward. The other equation is a²... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 210 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum depth of a perfect binary tree that can be isomorphic to Penchick's tree by using the given operations. Let me start by understanding the problem step by step.
First, the problem mentions that both trees must be isomorphic. Isomorphic trees have the same structure, mea... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 81 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's see. The problem is about a rhythm game called osu!mania where you have to process notes falling from the bottom to the top of the screen. Each row has exactly one note, represented by a '#', and we need to output the column of each note in the order they are processed.
First, I need to parse the input. T... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $\\alpha, \\beta, \\gamma, \\delta$ be real numbers such that $\\a... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 303 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out which of the given statements are true based on the problem. Let me start by understanding the problem step by step.
We have a plane defined by the equation αx + βy + γz = δ. The point (3, 2, -1) is the mirror image of the point (1, 0, -1) with respect to this plane. Also, we know... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 294 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have an array of integers and another array of probabilities, and we build a random multiset by inserting each element with a certain probability. Then, we need to compute the expected value of the square of the bitwise XOR of all elements in the multiset. The answ... |
[
{
"content": "Problem: Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$ , $AC=BD= \\sqrt{80}$ , and $BC=AD= \\sqrt{89}$ . There exists a point $I$ inside the tetrahedron such that the distances from $I$ to each of the faces of the tetrahedron are all equal. This distance can be written in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 28 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-28",
"reference_solution": "Notice that \\(41=4^2+5^2\\), \\(89=5^2+8^2\\), and \\(80=8^2+4^2\\), let \\(A~(0,0,0)\\), \\(B~(4,5,0)\\), \\(C~(0,5,8)\\), and \\(D~(4,0,8)\\). Then the plane \\(BCD\\) has a normal\n\\begin{equation*}\n\\mathbf n:=\\frac14\\overright... | <think>
Alright, so I need to find the distance from a point I inside a tetrahedron ABCD to each of its faces, given the edge lengths. The tetrahedron has edges AB, CD, AC, BD, BC, AD with lengths √41, √41, √80, √80, √89, √89 respectively. The point I is the incenter, equidistant from all faces. The distance should be ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 340 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where Alice and Bob play a game with n piles of stones. Each pile has a value a_i and a maximum number of stones b_i that can be in it. The game is about taking stones from the piles such that the number of stones taken follows certain conditions: you can take d stones i... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array nums of size n consisting of positive integers.\nYou are also given a 2D array queries of size m where queries[i] = [index_i, k... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 480 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to create a function that processes a series of queries on an array. The array starts with positive integers, and each query asks to mark a specific element and then mark some number of the smallest unmarked elements. After each query, I have to compute the sum of the unmarked elements. Let me b... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 68 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have a competition with n participants and m sports. Each participant has a skillset in some of these sports, represented by a binary string. The order of the sports is determined by a random number generator, and the competition proceeds such that if all remain... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Ringlet Wholesalers discounted its old line of dining-room sets at a chain discount of 30% and 10%. If the discount offered was $248.40, what was the... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 8 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the list price and the net price of the dining-room sets given that the chain discount is 30% and 10%, and the total discount offered is $248.40. Let me start by recalling how chain discounts work. A chain discount is when multiple discounts are applied successively. In this case, ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A compound with the molecular formula C8H9NO and the given NMR data is reacted with the following set of reagents:\n\n1. NaNO2 + HCl\n2. H2O\n3. aq. KOH, Heat \n\n1H-NMR... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 149 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's try to figure out this problem step by step. So, we have a compound with the molecular formula C8H9NO, and we need to identify the final product after it's reacted with NaNO2 + HCl, then H2O, and finally aq. KOH with heat. The 1H-NMR data is given, which might help us determine the structure.
First... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: In a photoelectric experiment a parallel beam of monochromatic... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 160 | JEEBench | {
"expected_answer": "24",
"problem_id": "13",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Alright, let's tackle this problem step by step. It's a photoelectric effect question with a twist involving forces on an anode. Okay, first, let me make sure I understand all the parts.
We have a parallel beam of monochromatic light with a power of 200 W incident on a perfectly absorbing cathode. The work fun... |
[
{
"content": "Problem: Find the largest possible real part of \\[(75+117i)z+\\frac{96+144i}{z}\\] where $z$ is a complex number with $|z|=4$ .\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 8,
"temperature": 0.7
} | 8 | 21 | AIME24 | {
"expected_answer": "540",
"problem_id": "aime24-21",
"reference_solution": "Let $z=a+bi$ such that $a^2+b^2=4^2=16$ . The expression becomes: \\[(75+117i)(a+bi)+\\dfrac{96+144i}{a+bi}.\\] Call this complex number $w$ . We simplify this expression. \\begin{align*}\nw&=(75+117i)(a+bi)+\\dfrac{96+144i}{a+bi} \... | <think>
Okay, so I need to find the largest possible real part of the expression \( (75 + 117i)z + \frac{96 + 144i}{z} \) where \( z \) is a complex number with \( |z| = 4 \). Hmm, let's break this down step by step.
First, since \( |z| = 4 \), I can write \( z \) in polar form. Let me recall that any complex number w... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 276 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let's tackle this problem. So, we have n cities in a row, each with a deadline a_i by which we need to conquer them. We can only conquer adjacent cities starting from a chosen starting city at time 1. The question is, how many starting cities allow us to win?
First, let me parse the problem again to m... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: In a radioactive decay chain, ${ }_{90}^{232} \\mathrm{Th}$ nucleus de... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 152 | JEEBench | {
"expected_answer": "AC",
"problem_id": "5",
"reference_solution": null,
"subject": "phy",
"type": "MCQ(multiple)"
} | <think>
Okay, so I need to figure out the number of alpha and beta particles emitted during the decay of a Thorium-232 nucleus into a Lead-212 nucleus. Let me start by recalling what alpha and beta decays involve.
Alpha decay is when a nucleus emits an alpha particle, which is equivalent to a helium-4 nucleus. This m... |
[
{
"content": "Problem: Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and\n \\[a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 6,
"temperature": 0.7
} | 6 | 10 | AIME24 | {
"expected_answer": "601",
"problem_id": "aime24-10",
"reference_solution": "$ab(a+b)+bc(b+c)+ac(a+c)=300(ab+bc+ac)-3abc=6000000, 100(ab+bc+ac)-abc=2000000$ Note that \n $(100-a)(100-b)(100-c)=1000000-10000(a+b+c)+100(ab+bc+ac)-abc=0$ . Thus, $a/b/c=100$ . There are $201$ cases for each but we need to subtrac... | <think>
Alright, so I need to find the number of triples of nonnegative integers (a, b, c) such that a + b + c = 300 and the sum a²b + a²c + b²a + b²c + c²a + c²b equals 6,000,000. Hmm, okay. Let me try to break this down step by step.
First, let's note that the equation a + b + c = 300 is straightforward. The other e... |
[
{
"content": "Problem: There exist constants $a$, $b$, $c$, and $d$ such that\n\\[(\\sin x)^7 = a \\sin 7x + b \\sin 5x + c \\sin 3x + d \\sin x\\]for all angles $x$. Find $d$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 64 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the constants a, b, c, and d such that (sin x)^7 can be expressed as a combination of sin 7x, sin 5x, sin 3x, and sin x. Specifically, the equation given is:
\[
(\sin x)^7 = a \sin 7x + b \sin 5x + c \sin 3x + d \sin x
\]
And I need to find the value of d. Hmm, this seems like a proble... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 160 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many days Little John is satisfied with the amount of milk he has. The problem gives me the number of test cases, each with a list of days and the amount of milk acquired on those days. The milk has a freshness of k days, so once acquired, it's drinkable for k days. John can dr... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is an election to choose one winner from N candidates with candidate numbers 1, 2, \\ldots, N, and there have be... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 329 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | from collections import defaultdict
def determine_winner(N, M, votes):
candidates = defaultdict(int)
current_winner = None
max_votes = 0
for i, vote in enumerate(votes, start=1):
candidates[vote] += 1
if candidates[vote] > max_votes:
max_votes = candidates[vote]
... |
[
{
"content": "Problem: What is the area of the region in the coordinate plane defined by\n$| | x | - 1 | + | | y | - 1 | \\le 1$?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 39 | AMC23 | {
"expected_answer": "8",
"problem_id": "49",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the area of the region defined by the inequality | |x| - 1 | + | |y| - 1 | ≤ 1. Hmm, that looks a bit complicated with all the absolute value signs. Let me try to break it down step by step.
First, let's simplify the expression inside the inequality. The term | |x| - 1 | is the absolute... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N roulette wheels.\nThe i-th (1\\leq i\\leq N) wheel has P _ i integers S _ {i,1},S _ {i,2},\\ldots,S _ {i,P... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 262 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where there are N roulette wheels, each with P_i integers written on them. The goal is to find the expected amount of money Takahashi will pay before he earns at least M points. The catch is that he has to minimize the amount of money he pays. Hmm, okay. Let me break thi... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 40 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out the number of valid permutations given the operations described. Let me start by understanding the problem step by step.
First, we have an initial permutation of size n, and we perform q operations on it. Each operation involves splitting a chosen array into two non-empty parts... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s. s[i] is either a lowercase English letter or '?'.\nFor a string t having length m containing only lowercase English letters, we defin... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 481 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to replace all the '?' characters in the string `s` with lowercase English letters such that the value of the modified string is minimized. If there are multiple strings with the same minimal value, I have to choose the lexicographically smallest one.
First, let me understand... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed array words containing n strings.\nLet's define a join operation join(x, y) between two strings x and y as concatenating them into xy... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 48 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to minimize the length of the string after performing n-1 join operations on the given list of words. Each operation can either concatenate the current string with the next word or vice versa, with the condition that if the last character of the current string matches the fi... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N people standing in a line. The person standing at the i-th position from the front is person P_i.\nProcess... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 391 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def process_queries():
import sys
def read_int():
return int(input())
def read_ints():
return list(map(int, input().split()))
N = read_int()
positions = read_ints()
Q = read_int()
queries = [read_ints() for _ in range(Q)]
for A, B in queries:
front_p... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to find a binary string of length n such that the oneness is as small as possible. Oneness is defined as the absolute difference between the number of non-empty subsequences that only contain 0s (f(t)) and the number of non-empty subsequences that contain at le... |
[
{
"content": "Problem: What is the value of\n\\[2^3 - 1^3 + 4^3 - 3^3 + 6^3 - 5^3 + \\dots + 18^3 - 17^3?\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 5,
"temperature": 0.7
} | 5 | 3 | AMC23 | {
"expected_answer": "3159",
"problem_id": "3",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I have this problem here: What is the value of the series 2³ - 1³ + 4³ - 3³ + 6³ - 5³ + … + 18³ - 17³. Hmm, let me try to figure this out step by step.
First, let me write down the series again to make sure I have it right. It alternates signs starting with a positive sign for the second term: +, -, ... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: An intelligent civilization in the Large Magellanic Cloud has engineered an extraordinary spacecraft capable of traveling at a substantial fraction of the speed of light... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 59 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how long it would take for an astronaut traveling at 0.99999987 times the speed of light to reach Earth from the Large Magellanic Cloud. The astronaut is 22 years old from their perspective, and I need to calculate the travel time considering relativistic effects. Let me recall som... |
[
{
"content": "Problem: Four points, $A$, $B$, $C$, and $D$, are chosen randomly and independently on the circumference of a circle. What is the probability that segments $AB$ and $CD$ intersect?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 323 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the probability that two randomly chosen segments, AB and CD, intersect on the circumference of a circle. Hmm, let's start by visualizing this. If I have four points A, B, C, D on the circle, when would the segments AB and CD cross each other?
I remember that two chords (which are the s... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: The minimum kinetic energy needed by an alpha particle to caus... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 394 | JEEBench | {
"expected_answer": "2.32",
"problem_id": "20",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I need to find the minimum kinetic energy required by an alpha particle (which is ${ }_{2}^{4} \mathrm{He}$) to cause the nuclear reaction with nitrogen-16 (${ }_{7}^{16} \mathrm{~N}$) in the laboratory frame. The products are a proton (${ }_{1}^{1} \mathrm{H}$) and oxygen-19 (${ }_{8}^{19} \mathrm{O}$... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 217 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which numbers on the board could have been the important integer n, which was supposed to be in the form 10^x where x is at least 2. But when Dmitry wrote it down, he missed the exponent symbol, so the numbers got messed up. The task is to check each number on the board and determi... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 212 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to solve this card game problem. Let me start by understanding the problem statement again.
We have two players, Suneet and Slavic. Each of them has two cards with values between 1 and 10. The game is played over two rounds where each player picks one of their two cards in ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $S$ be the sample space of all $3 \\times 3$ matrices with... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 213 | JEEBench | {
"expected_answer": "0.5",
"problem_id": "51",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to find the conditional probability \( P(E_1 \mid E_2) \). Let me recall that conditional probability is calculated as \( P(E_1 \mid E_2) = \frac{P(E_1 \cap E_2)}{P(E_2)} \). So, I need to find two things: the probability of both \( E_1 \) and \( E_2 \) happening, and the probability of \( E_2 \... |
[
{
"content": "Problem: Let $K$ be the number of sequences $A_1$, $A_2$, $\\dots$, $A_n$ such that $n$ is a positive integer less than or equal to $10$, each $A_i$ is a subset of $\\{1, 2, 3, \\dots, 10\\}$, and $A_{i-1}$ is a subset of $A_i$ for each $i$ between $2$ and $n$, inclusive. For example, $\\{\\}$, $\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 14 | AMC23 | {
"expected_answer": "5",
"problem_id": "16",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the number of sequences of subsets \( A_1, A_2, \ldots, A_n \) where each \( A_i \) is a subset of \( \{1, 2, \ldots, 10\} \), and each subsequent set \( A_{i-1} \) is a subset of \( A_i \). The value of \( n \) can be from 1 up to 10. Then, I need to find the remainder when this t... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: If $y(x)$ is the solution of the differential equation\n\\[\nx d y-\\left(y^{2}-4 y\\right) d x=0 \\text { for... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 413 | JEEBench | {
"expected_answer": "8",
"problem_id": "2",
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | <think>
Okay, so I need to solve this differential equation: \( x \, dy - (y^2 - 4y) \, dx = 0 \) with the initial condition \( y(1) = 2 \). Then, find \( 10 y(\sqrt{2}) \). Hmm, let's start by understanding the equation.
First, the equation is \( x \, dy - (y^2 - 4y) \, dx = 0 \). Maybe I can rewrite this to separate... |
[
{
"content": "Problem: For how many positive integers $n>1$ is it true that $2^{24}$ is a perfect $n^{\\text{th}}$ power?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 186 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out for how many positive integers n > 1, the number 2^24 is a perfect n-th power. Hmm, let me start by understanding what the problem is asking.
First, if 2^24 is a perfect n-th power, that means there exists some integer k such that k^n = 2^24. So, essentially, we need to find all ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a binary string s and a positive integer k.\nA substring of s is beautiful if the number of 1's in it is exactly k.\nLet len be the length of the... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 112 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to write a function that finds the lexicographically smallest beautiful substring in a given binary string `s` with exactly `k` ones. If no such substring exists, it should return an empty string. Let me break down the problem step by step.
First, let's understand what a beautiful substring ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S of length 16 consisting of 0 and 1.\nIf the i-th character of S is 0 for every even number i ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 294 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```python
def check_string():
import sys
def is_all_zeros(s):
for i in range(2, 17, 2): # even indices from 2 to 16
if s[i] != '0':
return False
return True
S = sys.stdin.readline().strip()
if is_all_zeros(S):
print("Yes")
else:
print("N... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums of positive integers and an integer k.\nIn one operation, you can remove the last element of the array and add it to your collectio... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 98 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out the minimum number of operations needed to collect elements 1 through k from the array nums. Each operation allows me to remove the last element and add it to my collection. The goal is to collect all elements from 1 to k with the least number of such operations. Let me break th... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Do treaties bind third States, ie non-State parties?\nOptions: A. Treaties do no create obligations or rights for third States without their consent,... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 432 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether treaties can bind third states, which are not parties to the treaty. Let me start by recalling some basic international law principles.
First, treaties are agreements between states. The main idea is that the parties to the treaty agree to certain obligations and rights t... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: The Pinacol-Pinacolone rearrangement is a chemical reaction involving the conversion of a pinacol molecule, containing two adjacent alcohol groups, into a pinacolone und... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 142 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, let me try to figure out this problem. So, the question is about the Pinacol-Pinacolone rearrangement. The starting materials and products are given in options A and B, and we need to determine which one is correct. Let me start by recalling what the Pinacol-Pinacolone rearrangement is.
From what I re... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Two players, $P_{1}$ and $P_{2}$, play a game against each other. In ever... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 390 | JEEBench | {
"expected_answer": "A",
"problem_id": "16",
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | <think>
Alright, let's tackle this probability problem. So, we have two players, P1 and P2, each rolling a fair die in each round. The outcomes are compared, and points are awarded accordingly: 5 points to the higher player, 0 to the lower; if they tie, both get 2 points. We need to find the probabilities listed in I t... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 237 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have a building with n floors, and people are launching paper airplanes. The goal is to find the number of ways to fill in the gaps in the records of who launched which airplane, such that the launches are consistent with the given constraints. Each floor can on... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 244 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where Iris has to compute the product of adjacent elements in a subarray and figure out the minimum number of operations needed to ensure that the product of any two adjacent elements doesn't exceed k. Wait, actually, the problem says that the array is modified so that t... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: The Traditional Religion Advocacy Party (TRAP) has successfully lobbied the State of Texarkana for a statute named \"Equal Rights for All Religions.\... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 67 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the strongest argument the American Atheism Association (AAA) can make against the "Equal Rights for All Religions" statute in Texarkana. Let me start by understanding the problem.
The statute requires broadcasters who air segments about Christianity to give equal time for segment... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Determine the starting material needed to synthesize 5-isopropyl-3,4-dimethylcyclohex-1-ene via ring-closing metathesis.\nOptions: A) 5-isopropyl-3,4-dimethylocta-1,6-di... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 53 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out which starting material is needed to synthesize 5-isopropyl-3,4-dimethylcyclohex-1-ene via ring-closing metathesis. Hmm, let's start by recalling what ring-closing metathesis (RCM) is. It's a reaction where a diene isomerizes to form a cyclic olefin, right? The key here is that the... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: Given the following Lagrangian\n\n\\mathcal{L}_{int}=\\kappa\\bar{\\psi}\\sigma_{\\mu\\nu}\\psi F^{\\mu\\nu}\n\nwhere \\sigma_{\\mu\\nu}=\\frac{i}{2}\\left[\\gamma_{\\mu... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 177 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the mass dimension of κ in the given Lagrangian and determine if the theory is renormalizable. Let me start by recalling some basic concepts.
First, the Lagrangian provided is the interaction term, which involves the product of the Dirac conjugate of a fermion field ψ, the antisym... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A synchrocyclotron is a special type of cyclotron. A proton is injected at \\$t=0\\$ with negligible kinetic energy, i.e. \\$T\\simeq0\\$ undergoes two accelerations in ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 136 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many revolutions a proton makes in a synchrocyclotron. The problem gives me the voltage applied as U(t) = U0*cos[2πν(α)t + Φ0], with U0 = 190kV and Φ0 = π/4. The proton starts with almost zero kinetic energy and ends up with T1 = 950MeV. Hmm, let's break this down step by step.... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 194 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the minimum number of operations required to make all numbers from l to r equal to zero. The operation is a bit tricky: we pick two numbers x and y, then replace them with 3x and floor(y/3). Hmm. Let me try to break this down step by step.
First, let me understand the operation. E... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Air is flowing perpendicularly to a pipe, transferring heat by forced convection. The pipe has a diameter 4 in. and a surface temperature of 90°F. Th... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 42 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to calculate the rate of heat transfer per unit length of a pipe that's being cooled by air flowing past it. The pipe has a diameter of 4 inches and a surface temperature of 90°F. The air is flowing at a velocity of 15 feet per second with a bulk temperature of 75°F. Hmm, let me recall the formu... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: At $143 \\mathrm{~K}$, the reaction of $\\mathrm{XeF}_{4}$ wit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 198 | JEEBench | {
"expected_answer": "19",
"problem_id": "32",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to figure out the total number of lone pairs of electrons in the molecule Y, which is formed when XeF₄ reacts with O₂F₂ at 143 K. Hmm, let's start by recalling some chemistry basics.
First, I should write down the chemical equation for the reaction. XeF₄ is xendifour, and O₂F₂ is oxygen difluo... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 260 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a matrix with non-negative integers, and we can perform operations where either we flip the XOR of a row or the XOR of a column, and then compute the minimum possible beauty of the matrix. The beauty is the sum of absolute differences of adjacent cells. Hmm.
... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.We have a sequence A=(A_1,A_2,\\dots,A_N) of length N. Initially, all the terms are 0.\r\nUsing an integer K given in... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 221 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import heapq
def compute_f(A, K):
B = sorted(A, reverse=True)
return sum(B[:K])
def process_updates(N, K, Q, updates):
A = [0] * N
max_heap = []
min_heap = []
sorted_indices = set(range(N))
result = []
for x, y in updates:
x -= 1 # Adjusting for 0-indexing
# Remove p... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 218 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where we have a sequence of integers and we can perform operations where we choose three consecutive elements, merge them into one element which is the maximum of the three plus 1. The goal is to calculate the maximum number of operations we can do without any element excee... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 15 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the maximum number of draws that could have happened in a game of chess between three friends, given their final scores. The problem states that the scores are non-decreasing, and I have to determine the maximum number of draws. If it's impossible, I should return -1. Let me start ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi has placed N gifts on a number line. The i-th gift is placed at coordinate A_i.\nYou will choose a half-open... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 313 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the maximum number of gifts I can collect by choosing a half-open interval [x, x + M) on a number line. The gifts are placed at coordinates A_i, and each has a value. The goal is to select an interval of length M that includes as many gifts as possible.
First, let's parse the pro... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 438 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how many ordered pairs of positive integers (a, b) there are such that a = n - b. Hmm, let me start by understanding the problem.
First, the problem states that for each test case, we're given an integer n, and we need to find the number of ordered pairs (a, b) where a and b are p... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two positive integers n and limit.\nReturn the total number of ways to distribute n candies among 3 children such that no child gets more than li... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 132 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to distribute n candies among 3 children such that no child gets more than limit candies. The question is asking for the total number of ways to do this. Let me think through this step by step.
First, let's understand the problem. We have three children, and we need to give... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You have n processors each having 4 cores and n * 4 tasks that need to be executed such that each core should perform only one task.\nGiven a 0-indexed integer... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 113 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out how to assign tasks to processors such that each core gets exactly one task, and the total time taken by all processors is minimized. Let me start by understanding the problem better.
We have n processors, each with 4 cores. So, there are 4n tasks in total, each with a certain exe... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S consisting of lowercase English letters and digits.\nS is guaranteed to end with 2023.\r\nCha... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 356 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | ```
def change_last_character():
S = input().strip() # Read the input string and strip leading/trailing whitespace
last_index = S.rfind('2023') # Find the last occurrence of '2023'
modified_string = S[:last_index] + '2024' # Change the last character (index 4) to 4
print(modified_string)
change_last... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer n denoting the total number of servers and a 2D 0-indexed integer array logs, where logs[i] = [server_id, time] denotes that the serve... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 38 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have n servers, some logs of requests, and a bunch of queries. The goal is to figure out for each query, how many servers didn't receive any requests in the interval [query_time - x, query_time]. Let me try to break this down step by step.
First, let me understand ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 121 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have to count the number of non-empty good arrays with elements from 1 to m, such that the GCD of the maximum values of all subarrays of length i is unique for every i. The problem is a bit complex, but let me try to break it down step by step.
First, the problem m... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 0-indexed string s and a dictionary of words dictionary. You have to break s into one or more non-overlapping substrings such that each substri... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 13 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out how to break the string `s` into the minimum number of extra characters using the words in the dictionary. Let me start by understanding the problem again.
We have a string `s` and a list of words called `dictionary`. The goal is to split `s` into one or more non-overlapping su... |
[
{
"content": "Problem: Janet rolls a standard $6$-sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal $3$? The final answer can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive inte... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 18 | AMC23 | {
"expected_answer": "265",
"problem_id": "20",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the probability that at some point during 4 rolls of a standard 6-sided die, the running total equals 3. Hmm, let me start by understanding the problem step by step.
First, a standard 6-sided die has faces numbered 1 through 6. When Janet rolls the die multiple times, she keeps a ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given an integer N. You can perform the following two types of operations:\n\n- Pay X yen to replace N with \\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 427 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum expected cost to reduce N to 0 by performing either of two operations: either paying X yen to halve N (floor division), or paying Y yen to roll a die and divide N by the die roll (1-6). The goal is to minimize the total expected cost.
Here's the step-by-step appr... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 244 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to figure out who wins this game between Alice and Bob. The problem is similar to the Nim game but with a twist where you can't take a number of stones that shares a common divisor greater than 1 with the current pile size. Hmm, okay. Let me try to break this down step by step.
First, let me... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 138 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this Nim game problem where Artem and Ruslan play on segments of an array. The goal is to determine, for each segment, the maximum number of piles Ruslan can remove such that Artem loses, along with the number of ways to do so. If it's impossible, we have to output -1. Let me try to bre... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Reaction of $\\mathbf{x} \\mathrm{g}$ of $\\mathrm{Sn}$ with $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 356 | JEEBench | {
"expected_answer": "1.23",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the value of y, which is the mass of nitrobenzene in grams. The problem involves a reaction where tin (Sn) reacts with HCl to form a salt, which then reacts with nitrobenzene (C6H5NO2) also in the presence of HCl to produce 1.29 grams of an organic salt. Hmm, let me try to break this dow... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A court is investigating the possible occurrence of an unlikely event T. The reliability of two independent witnesses called Alf and Bob is known to ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 454 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the probability that event T occurred given that both Alf and Bob say it occurred. The problem gives me the reliability of each witness: Alf tells the truth with probability α = 9/10, Bob with probability β = 9/10, and the prior probability of T is τ = 1/1000. Hmm, let's break this... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 227 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out whether it's possible to add a new integer point to an existing set of points on a line such that this new point becomes the closest to every point in the set. The set is given in ascending order, so each point has a unique position. The new point has to be different from all exist... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: You want to create a mouse embryonic chimera with induced pluripotent stem cells from somatic cells of various tissues. You are interested in the iPSCs fate in the embry... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 75 | GPQADiamond | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To determine the first thing noticed in this scenario, let's break down the experiment step by step:
1. **Objective**: Create a mouse embryonic chimera with iPSCs from various somatic tissues. Study the fate of iPSCs and their co-localization with apoptotic events using TUNEL-FITC staining and confocal microscopy.
2.... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a weighted undirected complete graph with N vertices numbered from 1 to N. The edge connecting vertices ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 273 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import sys
def solve():
N = int(input().strip())
D = [list(map(int, input().strip().split())) for _ in range(N)]
max_weight = 0
from itertools import combinations
edges = [(i, j) for i in range(N) for j in range(i+1, N)]
weights = [(D[i][j], i, j) for i, j in edges]
weights.sort(reverse=... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $f_1:(0, \\infty) \\rightarrow \\mathbb{R}$ and $f_2:(0, \... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 371 | JEEBench | {
"expected_answer": "6",
"problem_id": "46",
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | <think>
Okay, so I need to solve this problem where I have two functions, f₁ and f₂, defined on the interval (0, ∞). The question is asking for the value of 6m₂ + 4n₂ + 8m₂n₂, where m₂ and n₂ are the number of points of local minima and local maxima respectively of f₂ in the interval (0, ∞).
First, let me understand ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a positive integer N.\nFind the maximum value of a palindromic cube number not greater than N.\nHere, a ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 397 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | import math
def find_max_palindromic_cube(N):
def is_palindrome(s):
return s == s[::-1]
def is_cube(K):
x = round(K ** (1/3))
return x ** 3 == K
def to_digits(K):
return list(map(int, str(K)))
def check_palindrome(K):
digits = to_digits(K)
L = len(digi... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Consider a hydrogen-like ionized atom with atomic number $Z$ w... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 161 | JEEBench | {
"expected_answer": "3",
"problem_id": "14",
"reference_solution": null,
"subject": "phy",
"type": "Numeric"
} | <think>
Okay, so I need to find the atomic number Z of a hydrogen-like ionized atom where the energy difference between the n=2 to n=1 transition photon and the n=3 to n=2 transition photon is 74.8 eV. Also, the ionization energy of the regular hydrogen atom is given as 13.6 eV. Hmm, let me recall the formulas related ... |
[
{
"content": "Problem: For the eight counties listed below, what was the median number of students in $2005?$\n\n\\begin{tabular}[t]{|l|c|c|c|c|c|}\n\\multicolumn{6}{c}{\\textbf{Number of Students per County}}\\\\\\hline\n\\textbf{COUNTY}&\\textbf{$2001$}&\\textbf{$2002$}&\\textbf{$2003$}&\\textbf{$2004$}&\\tex... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 105 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to find the median number of students in 2005 for these eight counties. Let me recall that the median is the middle value when the numbers are arranged in order. Since there are eight counties, the median should be the average of the fourth and fifth values when they're sorted from smallest to l... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 173 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have two strings a and b of length n, and we have to answer q queries. Each query asks for the minimum number of operations needed to make the sorted substring of a from index l to r equal to the sorted substring of b from index l to r. An operation consists of ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 233 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have a string of digits, and I need to compute the minimum length of a string obtained by splitting each contiguous substring of length k into an even number of non-empty parts and then writing the parts in reverse order. Hmm, let me parse the problem again.
First,... |
[
{
"content": "Problem: What is the value of\n\\[2^3 - 1^3 + 4^3 - 3^3 + 6^3 - 5^3 + \\dots + 18^3 - 17^3?\\]\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 3 | AMC23 | {
"expected_answer": "3159",
"problem_id": "3",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to figure out the value of this series: 2³ - 1³ + 4³ - 3³ + 6³ - 5³ + ... + 18³ - 17³. Hmm, let me start by understanding the pattern here. The terms are alternating in sign, starting with positive, and each pair seems to be two consecutive odd numbers or even numbers? Wait, let's see. The first... |
[
{
"content": "Problem: Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$ , $AC=BD= \\sqrt{80}$ , and $BC=AD= \\sqrt{89}$ . There exists a point $I$ inside the tetrahedron such that the distances from $I$ to each of the faces of the tetrahedron are all equal. This distance can be written in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 28 | AIME24 | {
"expected_answer": "104",
"problem_id": "aime24-28",
"reference_solution": "Notice that \\(41=4^2+5^2\\), \\(89=5^2+8^2\\), and \\(80=8^2+4^2\\), let \\(A~(0,0,0)\\), \\(B~(4,5,0)\\), \\(C~(0,5,8)\\), and \\(D~(4,0,8)\\). Then the plane \\(BCD\\) has a normal\n\\begin{equation*}\n\\mathbf n:=\\frac14\\overright... | <think>
Okay, so I have this problem about a tetrahedron ABCD with given edge lengths: AB = CD = √41, AC = BD = √80, and BC = AD = √89. There's a point I inside the tetrahedron that's equidistant from all four faces, and I need to find this distance in a specific form and then compute m + n + p where the distance is m√... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 401 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Alright, so I need to solve this problem where we have a string of Ls and Rs, and we need to find an array that satisfies certain conditions based on the counts of distinct numbers in subarrays. Let me try to break this down step by step.
First, the problem states that for each test case, we have a string `s` ... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $G$ be a circle of radius $R>0$. Let $G_{1}, G_{2}, \\ldots, G_{n}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 423 | JEEBench | {
"expected_answer": "CD",
"problem_id": "12",
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | <think>
Alright, let me try to figure out this problem. So, we have a big circle G with radius R, and n smaller circles G1, G2, ..., Gn, each with radius r. All the smaller circles touch the big circle externally. Also, each smaller circle touches the next one in the sequence, forming a closed loop. The question is ask... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S consisting of three different characters: A, B, and C.\nAs long as S contains the string ABC ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 324 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | Here's the Python function based on the problem description. The function reads the input string, repeatedly removes the substring "ABC" from the leftmost position, and prints the final string once no more "ABC" substrings are present.
```python
def remove_abc_substrings(input_string):
while "ABC" in input_string:... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given an integer sequence A = (A_1, A_2, \\dots, A_N).\r\nCalculate the following expression:\n\\displaystyle ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 434 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to compute the sum of the maximum values of (A_j - A_i) for all pairs (i, j) where j > i. The key idea is to iterate through each element and calculate the contribution of each element A_i to the total sum.
Here's the step-by-step explanation:
1. **Understanding the Problem**: We need ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Select the best translation into predicate logic. Marco moves from Italy to Spain. (i: Italy; m: Marco; s: Spain; Mxyz: x moves to y from z)\nOptions... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 469 | MMLUPro | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, let's see. I need to translate the sentence "Marco moves from Italy to Spain" into predicate logic using the given symbols. The options provided are Mism, Mssi, Msim, Mmis, Mmsi, and Mims. Hmm, first, let me make sure I understand the problem correctly.
We have:
- i: Italy
- m: Marco
- s: Spain
- Mxyz: x... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 220 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_solution": "",
"subject": null,
"type": null
} | <think>
Okay, so I need to solve this problem where I have a strip of cells with numbers and directions 'L' or 'R'. The goal is to maximize the score by performing operations where I can choose a segment from index l to r where s_l is 'L' and s_r is 'R'. Then I add up the numbers from l to r and replace all the 's_i' i... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: For the electrochemical cell,\n\\[\n\\operatorname{Mg}(\\mathr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 134 | JEEBench | {
"expected_answer": "10",
"problem_id": "28",
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | <think>
Okay, so I need to find the value of x, which is the concentration of Mg²⁺ in the cell. The problem gives me the standard cell potential at 1 M concentration, which is 2.70 V, and when the Mg²⁺ concentration is changed to x M, the cell potential becomes 2.67 V. They also provide some constants: F/R is 11500 K/V... |
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