instruction stringlengths 20 15.7k | input stringclasses 1
value | output stringlengths 785 74.2k | system stringclasses 1
value | extra_info dict |
|---|---|---|---|---|
A rectangle having area $1$ is inscribed in a circle having area $2$. How long is the diagonal of the rectangle? | <think>
Okay, let's see. I have a problem where a rectangle with area 1 is inscribed in a circle with area 2. I need to find the length of the diagonal of the rectangle. Hmm. Let me start by recalling some basic geometry concepts.
First, if a rectangle is inscribed in a circle, that means all four corners of the rect... | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "math",
"index": 1229530,
"source": "OpenMathReasoning"
} | |
Consider the set of irreducible fractions A = {n/d | nβ€d and d β€ 10000 and gcd(n,d) = 1}.You are given a member of this set and your task is to find the largest fraction in this set less than the given fraction.
Note : this is a set and so all the members are unique.
Example 1:
Input: n = 1, d = 8
Output: 1249 9993
Exp... | <think>
Okay, I need to solve this problem where given a fraction n/d, which is part of the set A of irreducible fractions where numerator is β€ denominator and denominator β€10,000, I have to find the largest fraction in A that is less than n/d. And return it as a list of numerator and denominator.
Hmm. Let's think. T... | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "code",
"index": 3533887,
"source": "TACO"
} | |
A mischievous robot named Robo is on a mission to collect energy crystals from two different planets. On Planet X, each crystal gives E_x energy units and weighs W_x grams. On Planet Y, each crystal gives E_y energy units and weighs W_y grams. Robo's energy storage can hold a maximum of C grams of crystals without over... | <think>
Okay, let's see. The problem is about Robo collecting crystals from two planets to maximize energy without exceeding the weight limit. Hmm. So, the inputs are C, E_x, E_y, W_x, W_y. We need to find the maximum energy possible by choosing some number of crystals from X and Y such that their total weight is <= C.... | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "code",
"index": 3616569,
"source": "OpenCodeReasoning"
} | |
Donggyu wants to complete the diagram so that each box contains a positive integer and each box in the top two rows contains the product of the integers in the two boxes below it. He wants the integer in the top box to be 720. How many different values can the integer \( n \) take?
A. 1
B. 4
C. 5
D. 6
E. 8 | <think>
Okay, so Donggyu has this diagram that he wants to fill with positive integers. The structure is such that each box in the top two rows must be the product of the two boxes directly below it. The topmost box needs to be 720. The question is asking how many different values the integer n can take. The answer cho... | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "math",
"index": 3323741,
"source": "NuminaMath-CoT"
} | |
How many equivalence relations on the set of integers \( \mathbb{Z} \) contain the relation \( R \) defined by \( aRb \) if \( b = a + 3 \)? | <think>
Okay, let me try to figure out how many equivalence relations on the set of integers β€ contain the relation R defined by aRb if b = a + 3. Hmm, equivalence relations have to be reflexive, symmetric, and transitive. So first, I need to understand what R looks like.
R is the set of all pairs (a, a+3) where a is... | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "math",
"index": 454769,
"source": "OpenMathReasoning"
} | |
"One day Om Nom found a thread with n beads of different colors. He decided to cut the first several(...TRUNCATED) | "<think>\nOkay, I need to solve this problem where I have to determine for each prefix of a string w(...TRUNCATED) | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "code",
"index": 2391434,
"source": "OpenCodeReasoning"
} | |
"Given \\( x + y + z = 1 \\) and \\( xy + xz + yz = xyz \\), find the value of \\( \\frac{x^9 + y^9 (...TRUNCATED) | "<think>\nOkay, let's see. I have this problem where x, y, and z are three variables that add up to (...TRUNCATED) | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "math",
"index": 524218,
"source": "OpenMathReasoning"
} | |
"In the card game of blackjack played with a standard 52-card deck, the goal is to draw cards until (...TRUNCATED) | "<think>\nOkay, so I need to figure out how many possible unordered 3-card hands in blackjack add up(...TRUNCATED) | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "math",
"index": 3084370,
"source": "OpenMathReasoning"
} | |
"In the figure, the diagonals \\(AC\\) and \\(BD\\) of quadrilateral \\(ABCD\\) intersect at point \(...TRUNCATED) | "<think>\nOkay, so I have this geometry problem here. Let me try to visualize it first. There's a qu(...TRUNCATED) | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "math",
"index": 1962097,
"source": "NuminaMath-CoT"
} | |
"Let \\( R \\) be a \\( 20 \\times 18 \\) grid of points where adjacent points are 1 unit apart. A f(...TRUNCATED) | "<think>\nOkay, let me try to work through this problem step by step. First, let's make sure I under(...TRUNCATED) | Please reason step by step, and put your final answer within \boxed{}. | {
"category": "math",
"index": 2203828,
"source": "OpenMathReasoning"
} |
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π§ AceReason 11 100K
AceReason 11 100K is a dataset designed for fine-tuning and evaluating reasoning capabilities in small- to mid-scale large language models.
It includes diverse reasoning tasks spanning mathematics, logic, coding, and scientific reasoning.
π Dataset Summary
The dataset contains random 15000 samples out of 100,000 examples of reasoning prompts and completions.
Each example is formatted as JSON objects with fields like:
instruction: The user question or task.input: Optional additional context (may be empty).output: The expected or reference model response.
You can use it for instruction-tuning or reasoning evaluation.
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