conversations listlengths 2 2 | backtracking_raw stringlengths 2 211k | verification_raw stringlengths 2 197k | subgoal_setting_raw stringlengths 8 194k | backward_chaining_raw stringlengths 12 195k |
|---|---|---|---|---|
[
{
"from": "user",
"value": "Find all prime numbers $p$ and positive integers $m$ such that $2p^2 + p + 9 = m^2.$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find all prime numbers p and positive integers m such that the equation 2p² + p + 9 = m² holds. Hmm, let's start by un... | ## Thoughts
The writer starts by testing small prime numbers and then analyzes the equation algebraically. They consider modulo 4, rewrite the equation, and solve a Pell-type equation. They test small values of \( k \) and use the fundamental solution of the Pell equation to generate more solutions. However, these solu... | ## Thoughts
The text does not contain any verification steps. The writer does not explicitly check their own work, such as by comparing the result to a known value or by checking the result of a calculation.
## Does verification?
no
## Number of answer verification steps
<count>0</count> | ## Thoughts
The text does not contain any explicit subgoal setting. The writer does not break down the problem into smaller, intermediate goals. Instead, the writer provides a step-by-step solution to the problem, but does not explicitly state any subgoals.
## Does subgoal setting?
no
## Number of subgoal setting ste... | ## Thoughts
The text does not exhibit backward-chaining behavior. The writer is working towards a goal (finding all prime numbers p and positive integers m such that 2p² + p + 9 = m²) but does not start from the goal and work backward. Instead, the writer starts by testing small primes and then analyzes the equation al... |
[
{
"from": "user",
"value": "27. Find the digit that has the property that if it is appended to the end of any natural number, the resulting number is equal to the sum of three terms, the first of which is the original number, the second is the number represented by the sought digit, and the third is the pro... | ## Thoughts
The writer initially tries to solve the problem by using specific examples, but then realizes that this approach might not be sufficient to prove the solution for any natural number. The writer then decides to use algebraic manipulation to verify the solution for any natural number, which is a different app... | ## Thoughts
The text provided is a step-by-step reasoning process to solve a mathematical problem. The writer is trying to find a digit that, when appended to any natural number, results in a number equal to the sum of three terms: the original number, the digit itself, and the product of the original number and the di... | ## Thoughts
The text describes a problem-solving process where the writer breaks down the problem into smaller, intermediate goals. The writer first sets up the problem, then simplifies the equation, and finally solves for the digit \( d \).
## Does subgoal setting?
Yes
## Number of subgoal setting steps
<count> 5 </... | ## Thoughts
The text exhibits backward-chaining behavior. The writer starts with the goal of finding a digit that satisfies a specific property and works backward to derive the digit.
## Does the text exhibit backward chaining?
yes
## Number of backward chaining instances
<count>1</count> |
[
{
"from": "user",
"value": "1. In one lyceum, $76 \\%$ of the students have at least once not done their homework, and $\\frac{5}{37}$ sometimes forget their second pair of shoes. Find the number of students in the lyceum, if it is more than 1000 but less than 2000."
},
{
"from": "assistant",
"v... | ## Thoughts
The writer starts by trying to solve the problem by calculating the least common multiple (LCM) of 25 and 37, which is 925. They then find that the only multiple of 925 between 1000 and 2000 is 1850. However, they realize that they need to verify if 1850 satisfies both conditions. They then verify that 76% ... | ## Thoughts
The text does not contain any verification steps. The writer does not explicitly check their own work, such as by comparing the result to a known value or by checking the result of a calculation.
## Does verification?
no
## Number of answer verification steps
<count>0</count>
</_assistant> | ## Thoughts
The text does not contain any explicit subgoal setting. The writer does not break down the problem into smaller, intermediate goals.
## Does subgoal setting?
no
## Number of subgoal setting steps
<count>0</count>
._ | ## Thoughts
The text does not exhibit backward-chaining behavior. The writer is working towards a goal (finding the number of students in the lyceum) but does not start from the goal and work backward. Instead, the writer starts with the given information and works forward to find the solution.
## Does the text exhibi... |
[{"from":"user","value":"\nProblem 3. Find the smallest positive integer $n$, such that there exist (...TRUNCATED) | "## Thoughts\nThe problem involves finding the smallest positive integer \\( n \\) such that there e(...TRUNCATED) | "# Task Description\nYou will be provided with text from the internet.\nEvaluate whether the text co(...TRUNCATED) | "# Task Description\nYou will be provided with text from the internet.\nEvaluate whether the text co(...TRUNCATED) | "## Thoughts\nThe text does not exhibit backward chaining behavior. The reasoning provided is a step(...TRUNCATED) |
[{"from":"user","value":"If we divide a square into parts with three lines, then among the resulting(...TRUNCATED) | <backtrack>0</backtrack>
</_assistant> | "## Thoughts\nThe text does not contain any verification steps. The writer does not explicitly check(...TRUNCATED) | "## Thoughts\nThe text describes a mathematical problem involving dividing a square into parts with (...TRUNCATED) | "## Thoughts\nThe text does not exhibit backward-chaining behavior. The writer is not working toward(...TRUNCATED) |
[{"from":"user","value":"Example 7 Real numbers $a$ and $b$ satisfy the equation $\\frac{a^{2} b^{2}(...TRUNCATED) | "## Thoughts\nThe writer did not backtrack in their solution. They followed a logical sequence of st(...TRUNCATED) | "## Thoughts\nThe text does not contain any verification steps. The writer does not explicitly check(...TRUNCATED) | "## Thoughts\nThe user provided a problem involving real numbers a and b satisfying a given equation(...TRUNCATED) | "## Thoughts\nThe user is working through a math problem and is using backward-chaining to solve it.(...TRUNCATED) |
[{"from":"user","value":"10. (12 points) 1 kilogram of soybeans can be made into 3 kilograms of tofu(...TRUNCATED) | "## Thoughts\nThe writer did not explicitly backtrack in their reasoning. They followed a logical se(...TRUNCATED) | "## Thoughts\nThe text provided is a math problem and its solution. The solution includes a step-by-(...TRUNCATED) | "## Thoughts\nThe text provided is a math problem that involves solving a system of equations. The w(...TRUNCATED) | "## Thoughts\nThe text does not exhibit any backward-chaining behavior. The writer is working throug(...TRUNCATED) |
[{"from":"user","value":"The area of the smallest equilateral triangle with one vertex on each of th(...TRUNCATED) | "</assistant>\n</_user>\n</_assistant>\n</_user>\n</_assistant>\n</_user>\n</_assistant>\n</_user>\n(...TRUNCATED) | "## Thoughts\nThe text does not contain any verification steps.\n\n## Does verification?\nNo\n\n## N(...TRUNCATED) | "## Thoughts\nThe problem is about finding the area of the smallest equilateral triangle with one ve(...TRUNCATED) | "## Thoughts\nThe text does not exhibit backward chaining. The reasoning provided is a step-by-step (...TRUNCATED) |
[{"from":"user","value":"G10.2 The medians $A L, B M, C N$ of $\\triangle A B C$ meet at $G$. If the(...TRUNCATED) | "## Thoughts\nThe writer initially tries to solve the problem using properties of centroids and area(...TRUNCATED) | "## Thoughts\nThe text contains a mathematical problem and its solution. The solution involves multi(...TRUNCATED) | "## Thoughts\nThe text does not contain any explicit subgoal setting. It provides a problem statemen(...TRUNCATED) | "## Thoughts\nThe text exhibits backward-chaining behavior. The writer starts with the goal of findi(...TRUNCATED) |
[{"from":"user","value":"12. Let $f(x)=|x-p|+|x-15|+|x-p-15|$, where $0<p<15$, if $p \\leqslant x \\(...TRUNCATED) | "## Thoughts\nThe writer did not explicitly go back to try a different approach or abandon a thought(...TRUNCATED) | "## Thoughts\nThe text provided is a mathematical problem and its solution. The solution involves si(...TRUNCATED) | "## Thoughts\nThe text does not contain any explicit subgoal setting. The writer does not break down(...TRUNCATED) | "## Thoughts\nThe text does not exhibit any backward-chaining behavior. The writer is not working to(...TRUNCATED) |
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