🧩 Python Logic Puzzle

HARD

Solve the recursive mystery

📋 Challenge Description

A mysterious Python function has been found in an old codebase. The function seems to perform some complex calculations, but its true purpose is hidden. Your task is to understand what this function does and find the specific input that produces the magic number.


Objective: Determine what input to the function will result in the output 42069. The input is a positive integer between 1 and 10000.

📄 mystery.py 
def mystery_function(n):
    # A mysterious recursive function
    if n <= 0:
        return 0
    elif n == 1:
        return 1
    elif n == 2:
        return 3
    else:
        # The mystery lies here...
        result = 0
        for i in range(1, n):
            if n % i == 0:
                result += i
        
        if result == n:
            return n * n + mystery_function(n - 1)
        elif result > n:
            return n * 3 + mystery_function(n - 2)
        else:
            return n + mystery_function(n - 1)

# What value of x makes mystery_function(x) == 42069?
# The answer is the flag!

🎯 Your Mission:

Target Output: 42069
Input Range: A positive integer between 1 and 10000
Task: Find the input value x where mystery_function(x) == 42069
Flag Format: CTF{x} where x is the answer

💡 Hints to Get Started:

1. Understand the Logic: The function checks if a number is perfect (sum of divisors equals n), abundant (sum > n), or deficient (sum < n).
2. Perfect Numbers: 6, 28, 496, 8128... are perfect numbers (sum of proper divisors equals the number).
3. Write a Script: You'll need to test different values. A chatbot can help you write code to iterate and test values.
4. Optimization: You can use memoization or dynamic programming to speed up the calculation.
5. Test Small Values: Try mystery_function(10), mystery_function(20), etc. to understand the pattern.
6. Ask a Chatbot: "Help me find what input to this function gives output 42069" and provide the code.
💻 Testing Template 
# Use this template to test values

def mystery_function(n):
    # ... (copy the function above)
    pass

# Test different values
for i in range(1, 10001):
    result = mystery_function(i)
    if result == 42069:
        print(f"Found it! Input: {i}")
        break
    if i % 100 == 0:
        print(f"Testing {i}... current result: {result}")
Flag Format: CTF{answer_number}