completion stringlengths 2.5k 39.4k | query stringlengths 1.41k 7.24k |
|---|---|
<think>
Okay, let's try to tackle this problem step by step. First, I need to understand what's given and what needs to be found.
We have triangle ABC with angle A having a sine of 4/5, and angle A is acute. So, angle A is less than 90 degrees. Then there's a point D outside the triangle such that AD is the angle bis... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step using the given cheatsheet. The question is about finding the expected area of triangle AXY where X and Y are random points on the perimeter of a unit square ABCD. The answer needs to be in the form m/n and then compute m + n.
First, I need to recall the relev... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem step by step using the given cheatsheet. The problem involves two pairs of quadratic equations sharing common roots, and we need to find the sum a + b + c where a, b, c are distinct numbers.
First, let me parse the problem again. We have:
1. The equations x² + a x + 1 = 0... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to figure out this problem step by step. So, there are 7 boxes arranged in a row, numbered 1 to 7. We have 2015 cards to distribute, placing them one by one following a specific pattern. The first card goes into box 1, then 2, up to 7. Then we go back, placing the 8th card in box 6, 9th in 5, an... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to solve this problem. The question is about finding the sum over all triples (a, b, c) of non-negative integers where a + b + c is even, of the term 1/(2^a 3^b 5^c). Then express that sum as a reduced fraction m/n and find m + n.
First, I need to understand the problem. We have three variables... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to figure out for which integers n the polynomial n⁴ + 6n³ + 11n² + 3n + 31 is a perfect square. Hmm, the problem is asking when this quartic polynomial equals some integer squared.
First, I remember from the cheatsheet that when dealing with high-degree polynomials that might be perfect squar... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to tackle this problem step by step. The question is about finding the smallest possible value of d, given four positive integers a, b, c, d where a < b < c < d. The condition is that the arithmetic mean of a, b, c is half of the arithmetic mean of a, b, c, d.
First, I need to translate the giv... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
<think>
Okay, let's try to tackle this problem step by step. The question is about n coins arranged in a circle. The allowed operation is flipping two neighboring coins if they are both heads or both tails. We need to find the number of distinct arrangements where no arrangement can be transformed into another using th... | <|im_start|>user
# GENERATOR (PROBLEM SOLVER)
Instruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:
1. A specific question or problem to solve
2. A cheatsheet containin... |
"<think>\nOkay, let's try to figure out this problem. The question is asking for the smallest prime (...TRUNCATED) | "<|im_start|>user\n# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving as(...TRUNCATED) |
"<think>\nOkay, let's try to tackle this problem step by step. First, I need to understand what's gi(...TRUNCATED) | "<|im_start|>user\n# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving as(...TRUNCATED) |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 1