p-doom/crowd-code-dataset-0.2 huggingface dataset:
[content] easy_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

The probability of snow 
on 1st January is 1/20. What is the probability that snow will fall on the next 1st January?"}], "output": "## Step 1: Understand the problem
The problem asks for t
he probability that it will snow on the next 1st January, given the probability of snow on any 1st January is 1/20.

## Step 2: Determine the probability for the n
ext year
Since the probability of snow on any given 1st January is 1/20, this probability applies to every year, including the next one.

## Step 3: Apply the pro
bability to the next year
The probability that it will snow on the next 1st January is the same as for any 1st January, which is given as 1/20.

The final answer 
is: $\\boxed{\\frac{1}{20}}$", "category": "math", "license": "cc-by-4.0", "reasoning": "off", "generator": "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt
": "detailed thinking off", "used_in_training": "Ulta, Super, Nano"}
[content] easy_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

When orange trees are pl
anted to the acre, each tree yields 100 pounds of fruit. For each additional tree over 100, the yield per tree is reduced by 1 pound. How many trees should be plante
d so that the yield per acre is 4816 pounds?"}], "output": "## Step 1: Define the variables and the problem
Let's denote the number of trees planted per acre as \\(
T\\). The yield per tree can be represented as \\(100 - (T - 100)\\) pounds for \\(T > 100\\), since for each additional tree over 100, the yield per tree decreases 
by 1 pound.

## Step 2: Formulate the equation based on the given conditions
The total yield per acre is given as 4816 pounds. Therefore, we can set up the equati
on \\(T \	imes (100 - (T - 100)) = 4816\\).

## Step 3: Simplify the equation
Simplifying the equation gives us \\(T \	imes (200 - T) = 4816\\), which further s
implifies to \\(200T - T^2 = 4816\\).

## Step 4: Rearrange the equation into a standard quadratic form
Rearranging the equation gives us \\(T^2 - 200T + 4816 = 0
\\).

## Step 5: Solve the quadratic equation
To solve \\(T^2 - 200T + 4816 = 0\\), we can use the quadratic formula: \\(T = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}
\\), where \\(a = 1\\), \\(b = -200\\), and \\(c = 4816\\).

## Step 6: Plug the values into the quadratic formula
Substituting the values into the formula gives 
us \\(T = \\frac{-(-200) \\pm \\sqrt{(-200)^2 - 4 \\cdot 1 \\cdot 4816}}{2 \\cdot 1}\\), which simplifies to \\(T = \\frac{200 \\pm \\sqrt{40000 - 19264}}{2}\\).


## Step 7: Simplify under the square root
Further simplification yields \\(T = \\frac{200 \\pm \\sqrt{20736}}{2}\\), which then becomes \\(T = \\frac{200 \\pm 144}{
2}\\).

## Step 8: Solve for T
This gives us two solutions: \\(T = \\frac{200 + 144}{2} = 172\\) and \\(T = \\frac{200 - 144}{2} = 28\\). Since the number of tree
s cannot be negative and the yield reduction starts after 100 trees, the valid solution is \\(T = 172\\), but we need to check if this solution fits the initial cond
ition of the yield per acre being 4816 pounds.

## Step 9: Verify the solution fits the context
Given that for each tree over 100, the yield per tree decreases by
 1 pound, planting 172 trees would indeed reduce the yield per tree. We should verify if 172 trees yield 4816 pounds: \\(172 \	imes (100 - (172 - 100)) = 172 \	ime
s (100 - 72) = 172 \	imes 28 = 4816\\). This confirms that 172 trees will yield 4816 pounds per acre.

The final answer is: $\\boxed{172}$", "category": "math", "
license": "cc-by-4.0", "reasoning": "off", "generator": "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt": "detailed thinking off", "used_in_training": "Ult
a, Super, Nano"}
[content] easy_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

Let \\( X \\) be a set o
f 11 members. Let \\( P \\) be the collection of subsets of \\( X \\) which have three or more members. Is it possible to arrange all the members of \\( P \\) in a s
equence such that each member of the sequence is either its predecessor minus one member or its predecessor plus one member?"}], "output": "## Step 1: Understand the
 problem statement
The problem asks whether it's possible to arrange all subsets of a set \\( X \\) with 11 members, where each subset has three or more members, in
 a sequence such that each subset is either one member larger or one member smaller than the previous subset.

## Step 2: Determine the total number of subsets
To
 calculate the total number of subsets of \\( X \\) that have three or more members, we can use the formula for combinations since the order does not matter. The for
mula for combinations is \\( C(n, k) = \\frac{n!}{k!(n-k)!} \\), where \\( n \\) is the total number of items, \\( k \\) is the size of the subset, and \\( ! \\) den
otes factorial. We sum these combinations for \\( k = 3 \\) to \\( k = 11 \\) to get the total number of subsets.

## Step 3: Consider the requirements for the seq
uence
For a subset to be its predecessor minus one member or plus one member, there must be a specific relationship between the subsets that allows for this increme
ntal change. This typically involves subsets that differ by exactly one element.

## Step 4: Analyze the feasibility based on subset sizes
Given that the sequence
 must start with a subset of size 3 and can go up to subsets of size 11, we must consider how subsets can be arranged to satisfy the condition. The condition implies
 a \"chain\" of subsets where each is a subset or a superset of the previous one, differing by exactly one element.

## Step 5: Consider the limitations and constr
aints
Since each subset must differ from its predecessor by exactly one member, and given the vast number of subsets, especially of larger sizes, the arrangement wo
uld require a very specific and gradual increase or decrease in subset size. This becomes increasingly complex as the size of the subsets increases, especially consi
dering the need to maintain the \"one member difference\" rule.

## Step 6: Evaluate the possibility of such an arrangement
Given the constraints and the nature o
f combinations, we must assess whether it's mathematically feasible to create such a sequence that meets the criteria for all subsets of \\( X \\) with three or more
 members.

The final answer is: $\\boxed{No}$", "category": "math", "license": "cc-by-4.0", "reasoning": "off", "generator": "Llama-3.3-70B-Instruct", "version": "
v1", "system_prompt": "detailed thinking off", "used_in_training": "Ulta, Super, Nano"}
[content] hard_problems.jsonl (jsonl)

{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

Let \\( X \\) be a set of 11 members. Let \\( P \\) be the collection of subsets of \\( X \\) which have three or more members. Is it possible to arrange all the members of \\( P \\) in a sequence such that each member of the sequence is either its predecessor minus one member or its predecessor plus one member?"}], "output": "## Step 1: Understand the problem statement
The problem asks whether it's possible to arrange all subsets of a set \\( X \\) with 11 members, where each subset has three or more members, in a sequence such that each subset is either one member larger or one member smaller than the previous subset.

## Step 2: Determine the total number of subsets
To calculate the total number of subsets of \\( X \\) that have three or more members, we can use the formula for combinations since the order does not matter. The formula for combinations is \\( C(n, k) = \\frac{n!}{k!(n-k)!} \\), where \\( n \\) is the total number of items, \\( k \\) is the size of the subset, and \\( ! \\) denotes factorial. We sum these combinations for \\( k = 3 \\) to \\( k = 11 \\) to get the total number of subsets.

## Step 3: Consider the requirements for the sequence
For a subset to be its predecessor minus one member or plus one member, there must be a specific relationship between the subsets that allows for this incremental change. This typically involves subsets that differ by exactly one element.

## Step 4: Analyze the feasibility based on subset sizes
Given that the sequence must start with a subset of size 3 and can go up to subsets of size 11, we must consider how subsets can be arranged to satisfy the condition. The condition implies a \"chain\" of subsets where each is a subset or a superset of the previous one, differing by exactly one element.

## Step 5: Consider the limitations and constraints
Since each subset must differ from its predecessor by exactly one member, and given the vast number of subsets, especially of larger sizes, the arrangement would require a very specific and gradual increase or decrease in subset size. This becomes increasingly complex as the size of the subsets increases, especially considering the need to maintain the \"one member difference\" rule.

## Step 6: Evaluate the possibility of such an arrangement
Given the constraints and the nature of combinations, we must assess whether it's mathematically feasible to create such a sequence that meets the criteria for all subsets of \\( X \\) with three or more members.

The final answer is: $\\boxed{No}$", "category": "math", "license": "cc-by-4.0", "reasoning": "off", "generator": "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt": "detailed thinking off", "used_in_training": "Ulta, Super, Nano"}
[content] easy_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

Find the smallest prime 
number \\( p \\) such that \\( p \\) divides \\( n^2 + 7n + 23 \\)."}], "output": "## Step 1: Understand the problem statement
We are asked to find the smallest pri
me number \\( p \\) that divides the quadratic expression \\( n^2 + 7n + 23 \\).

## Step 2: Consider the nature of the quadratic expression
The given expression 
is a quadratic equation in the form of \\( n^2 + 7n + 23 \\). To find a prime \\( p \\) that divides this expression, we should consider how the expression could be 
factored or how it behaves for different values of \\( n \\).

## Step 3: Attempt to factor the quadratic expression
The quadratic expression \\( n^2 + 7n + 23 \\
) does not easily factor into the product of two binomials with integer coefficients. This suggests that we may need to consider the expression's discriminant or its
 behavior for specific values of \\( n \\) to understand its divisibility properties.

## Step 4: Consider the discriminant of the quadratic expression
The discri
minant \\( D \\) of a quadratic equation \\( ax^2 + bx + c = 0 \\) is given by \\( D = b^2 - 4ac \\). For the given expression, \\( a = 1 \\), \\( b = 7 \\), and \\(
 c = 23 \\). Therefore, \\( D = 7^2 - 4(1)(23) = 49 - 92 = -43 \\). Since the discriminant is negative, the quadratic equation has no real roots, meaning it does not
 cross the x-axis and is always positive or always negative for all real \\( n \\).

## Step 5: Examine the expression for specific values of \\( n \\) to find div
isibility by a prime
Given that the discriminant is negative and the expression does not factor easily, we can try substituting specific values of \\( n \\) to see 
if we can find a pattern or a prime divisor. Starting with small integers for \\( n \\) (e.g., \\( n = 0, 1, -1 \\)) can provide insights.

## Step 6: Evaluate the
 expression for \\( n = 0 \\)
For \\( n = 0 \\), the expression becomes \\( 0^2 + 7(0) + 23 = 23 \\). The number 23 is itself a prime number.

## Step 7: Determin
e if \\( p = 23 \\) is the smallest prime divisor
Since 23 is a prime number and it divides the expression when \\( n = 0 \\), we have found a prime number that sat
isfies the condition. Given its direct derivation from the expression, it is likely the smallest prime that does so, as smaller primes would not divide 23.

The fi
nal answer is: $\\boxed{23}$", "category": "math", "license": "cc-by-4.0", "reasoning": "off", "generator": "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt
": "detailed thinking off", "used_in_training": "Ulta, Super, Nano"}
[content] easy_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

Is there a geometric tra
nsformation that maps every point to exactly one point such that any triangle can be transformed into another triangle with the same area? (Alternatively, can any tr
iangle be transformed into a regular triangle with the same area?)"}], "output": "\\yes", "category": "math", "license": "cc-by-4.0", "reasoning": "off", "generator"
: "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt": "detailed thinking off", "used_in_training": "Ulta, Super, Nano"}
[content] easy_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

How many natural numbers
 greater than 6 but less than 60 are relatively prime to 15?"}], "output": "## Step 1: Determine the range of numbers
We are looking for natural numbers greater tha
n 6 but less than 60, which means we are considering the numbers from 7 to 59.

## Step 2: Identify the prime factors of 15
The prime factors of 15 are 3 and 5.


## Step 3: Calculate the total number of natural numbers in the range
There are 53 natural numbers from 7 to 59 (59 - 7 + 1 = 53).

## Step 4: Calculate the num
ber of multiples of 3 in the range
The first multiple of 3 in the range is 9, and the last is 57. The number of multiples of 3 is calculated as (57 - 9) / 3 + 1 = 1
7.

## Step 5: Calculate the number of multiples of 5 in the range
The first multiple of 5 in the range is 10, and the last is 55. The number of multiples of 5 is
 calculated as (55 - 10) / 5 + 1 = 10.

## Step 6: Calculate the number of multiples of 15 in the range
The first multiple of 15 in the range is 15, and the last 
is 45. The number of multiples of 15 is calculated as (45 - 15) / 15 + 1 = 3.

## Step 7: Apply the principle of inclusion-exclusion
To find the number of natural
 numbers that are not relatively prime to 15, we add the number of multiples of 3 and 5 and then subtract the number of multiples of 15 (since they were counted twic
e). This gives 17 + 10 - 3 = 24.

## Step 8: Calculate the number of natural numbers relatively prime to 15
The total number of natural numbers in the range is 53
, and 24 of them are not relatively prime to 15. So, the number of natural numbers relatively prime to 15 is 53 - 24 = 29.

The final answer is: $\\boxed{29}$", "c
ategory": "math", "license": "cc-by-4.0", "reasoning": "off", "generator": "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt": "detailed thinking off", "used
_in_training": "Ulta, Super, Nano"}
[content] hard_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

John picks two random in
tegers \\(a\\) and \\(b\\) such that \\(0 < a, b < 5\\) and \\(a + b = 5\\). Find the sum of all distinct values of \\(|a + bi| - |a + b + i(a + b)|\\)."}], "output"
: "## Step 1: Identify the possible values of \\(a\\) and \\(b\\)
Given \\(0 < a, b < 5\\) and \\(a + b = 5\\), we can list all possible integer pairs of \\((a, b)\
\) that satisfy these conditions. The pairs are: \\((1, 4)\\), \\((2, 3)\\), \\((3, 2)\\), and \\((4, 1)\\).

## Step 2: Calculate \\(|a + bi|\\) for each pair
Fo
r each pair, calculate the magnitude of the complex number \\(a + bi\\).
- For \\((1, 4)\\), \\(|1 + 4i| = \\sqrt{1^2 + 4^2} = \\sqrt{17}\\).
- For \\((2, 3)\\), \
\(|2 + 3i| = \\sqrt{2^2 + 3^2} = \\sqrt{13}\\).
- For \\((3, 2)\\), \\(|3 + 2i| = \\sqrt{3^2 + 2^2} = \\sqrt{13}\\).
- For \\((4, 1)\\), \\(|4 + 1i| = \\sqrt{4^2 +
 1^2} = \\sqrt{17}\\).

## Step 3: Calculate \\(|a + b + i(a + b)|\\) for each pair
Given \\(a + b = 5\\), calculate the magnitude of the complex number \\(5 + 5i
\\).
- For all pairs, since \\(a + b = 5\\), \\(|5 + 5i| = \\sqrt{5^2 + 5^2} = \\sqrt{50} = 5\\sqrt{2}\\).

## Step 4: Calculate \\(|a + bi| - |a + b + i(a + b)|\
\) for each pair
- For \\((1, 4)\\) and \\((4, 1)\\), \\(\\sqrt{17} - 5\\sqrt{2}\\).
- For \\((2, 3)\\) and \\((3, 2)\\), \\(\\sqrt{13} - 5\\sqrt{2}\\).

## Step
 5: Find the distinct values
There are two distinct values from the calculations: \\(\\sqrt{17} - 5\\sqrt{2}\\) and \\(\\sqrt{13} - 5\\sqrt{2}\\).

## Step 6: Sum
 the distinct values
Sum these distinct values to find the final answer.
\\(\\sqrt{17} - 5\\sqrt{2} + \\sqrt{13} - 5\\sqrt{2}\\).

## Step 7: Simplify the expres
sion
Combine like terms: \\(\\sqrt{17} + \\sqrt{13} - 10\\sqrt{2}\\).

The final answer is: $\\boxed{\\sqrt{17} + \\sqrt{13} - 10\\sqrt{2}}$", "category": "math",
 "license": "cc-by-4.0", "reasoning": "off", "generator": "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt": "detailed thinking off", "used_in_training": "U
lta, Super, Nano"}
[content] easy_problems.jsonl (jsonl)
{"input": [{"role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.

What is the total volume
 in cubic feet of three boxes if each box is a cube with edge length 4 feet?"}], "output": "## Step 1: Determine the formula for the volume of a cube
The volume \\(
V\\) of a cube is given by the formula \\(V = a^3\\), where \\(a\\) is the length of an edge of the cube.

## Step 2: Calculate the volume of one cube
Given that 
the edge length of each cube is 4 feet, we can substitute \\(a = 4\\) into the volume formula to find the volume of one cube. So, \\(V = 4^3 = 64\\) cubic feet.

#
# Step 3: Calculate the total volume of three cubes
To find the total volume of three identical cubes, we multiply the volume of one cube by 3. Therefore, the total
 volume is \\(64 \	imes 3 = 192\\) cubic feet.

The final answer is: $\\boxed{192}$", "category": "math", "license": "cc-by-4.0", "reasoning": "off", "generator":
 "Llama-3.3-70B-Instruct", "version": "v1", "system_prompt": "detailed thinking off", "used_in_training": "Ulta, Super, Nano"}
[content] check_problem_difficulty.py (python)
#!/usr/bin/env python3
"""
Script to process JSONL files and print file names and entries.
"""

import json
import sys
import argparse


def process_jsonl_file(file_path):
    """Process a single JSONL file and print its entries."""
    print(f"
{'='*60}")
    print(f"Processing file: {file_path}")
    print(f"{'='*60}
")
    
    try:
        with open(file_path, 'r', encoding='utf-8') as f:
            for line_num, line in enumerate(f, start=1):
                line = line.strip()
                if not line:  # Skip empty lines
                    continue
                
                try:
                    entry = json.loads(line)
                    print(f"Entry {line_num}:")
                    print(json.dumps(entry, indent=2))
                    print("-" * 60)
                except json.JSONDecodeError as e:
                    print(f"Error parsing entry on line {line_num}: {e}")
                    print(f"Line content: {line}")
                    print("-" * 60)
    except FileNotFoundError:
        print(f"Error: File '{file_path}' not found.")
    except Exception as e:
        print(f"Error processing file '{file_path}': {e}")


def main():
    parser = argparse.ArgumentParser(
        description='Process JSONL files and print file names and entries.'
    )
    parser.add_argument(
        'files',
        nargs='+',
        help='One or more JSONL files to process'
    )
    
    args = parser.parse_args()
    
    for file_path in args.files:
        process_jsonl_file(file_path)


if __name__ == '__main__':
    main()
[content] check_problem_difficulty.py (python)

    prompt = f"""
    You are a helpful assistant that determines the difficulty of a math problem.
    The problem is: {problem}
    Return the difficulty of the problem on a scale of 1 to 10, where 1 is the easiest and 10 is the hardest.
    """
    response = gemini.generate_content(prompt)
    return response.text