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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
6
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["## 1. ANALYSIS & STRATEGY\n\nWe are given a self-referential logic puzzle involving **11 students*(...TRUNCATED)
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
n!
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["## 1. ANALYSIS & STRATEGY\n\nWe are given a combinatorics problem from the 43rd IMO Shortlist 2002(...TRUNCATED)
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
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3426576
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["## 1. ANALYSIS & STRATEGY\n\n### Step 1: Understand the Problem\nWe are asked to find the number o(...TRUNCATED)
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
1012
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["## 1. ANALYSIS & STRATEGY\n\nWe are given a recurrence relation for an infinite sequence of intege(...TRUNCATED)
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
103
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["## 1. ANALYSIS & STRATEGY\n\nWe are given a problem involving four consecutive natural numbers $ N(...TRUNCATED)
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|
"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
51
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["We are continuing the solution from the prefix and need to complete the counting of valid ordering(...TRUNCATED)
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
4\sqrt{3}-6
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["## 1. ANALYSIS & STRATEGY\n\nWe are given a geometric problem involving cutting corners of an equi(...TRUNCATED)
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| 0.625
| 0.625
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| 0.999953
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| 1
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
f(n)=n^k
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["### **1. ANALYSIS & STRATEGY**\n\nWe are given a function $ f: \\mathbb{N} \\to \\mathbb{N} $ sati(...TRUNCATED)
| [1.0,1.0,1.0,1.0,0.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED)
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| 0.90625
| 0.90625
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
-\frac{1}{e^2}
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["# **Solution to the Problem**\n\nWe are given the function:\n\n$$\nf(x) = -\\frac{\\ln x}{x} + e^{(...TRUNCATED)
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| 0.75
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| 1
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"You are an expert in solving math problems. You are given a math problem and a solution prefix for (...TRUNCATED)
|
45
| "<|im_start|>user\nYou are an expert in solving math problems. You are given a math problem and a so(...TRUNCATED)
| ["### ✅ Final Solution: Area of the Section\n\nWe are given a **regular quadrilateral pyramid** wi(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED)
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