100 prisoners problem

gistfile1.txt

import random

def create_boxes():
    """ Create a list of 100 boxes, each containing a unique number from 1 to 100. """
    numbers = list(range(1, 101))
    random.shuffle(numbers)
    return numbers

def find_number(boxes, prisoner_number):
    """ Simulate a prisoner trying to find their number using the loop strategy. """
    current_box = prisoner_number - 1  # Box index starts from 0
    for _ in range(50):
        if boxes[current_box] == prisoner_number:
            return True
        current_box = boxes[current_box] - 1
    return False

def simulate_prisoners():
    """ Simulate all 100 prisoners trying to find their numbers. """
    boxes = create_boxes()
    for prisoner_number in range(1, 101):
        if not find_number(boxes, prisoner_number):
            return False
    return True

def run_simulations(n_simulations):
    """ Run multiple simulations and calculate the success rate. """
    success_count = 0
    for _ in range(n_simulations):
        if simulate_prisoners():
            success_count += 1
    return success_count / n_simulations

# Run 1000 simulations to estimate the success rate
n_simulations = 1000
success_rate = run_simulations(n_simulations)
print(f"Success rate over {n_simulations} simulations: {success_rate:.2%}")