Python/project_euler/problem_205/sol1.py

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"""
Project Euler Problem 205: https://projecteuler.net/problem=205
Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4.
Colin has six six-sided (cubic) dice, each with faces numbered 1, 2, 3, 4, 5, 6.
Peter and Colin roll their dice and compare totals: the highest total wins.
The result is a draw if the totals are equal.
What is the probability that Pyramidal Peter beats Cubic Colin?
Give your answer rounded to seven decimal places in the form 0.abcdefg
"""
from itertools import product
def total_frequency_distribution(sides_number: int, dice_number: int) -> list[int]:
"""
Returns frequency distribution of total
>>> total_frequency_distribution(sides_number=6, dice_number=1)
[0, 1, 1, 1, 1, 1, 1]
>>> total_frequency_distribution(sides_number=4, dice_number=2)
[0, 0, 1, 2, 3, 4, 3, 2, 1]
"""
max_face_number = sides_number
max_total = max_face_number * dice_number
totals_frequencies = [0] * (max_total + 1)
min_face_number = 1
faces_numbers = range(min_face_number, max_face_number + 1)
for dice_numbers in product(faces_numbers, repeat=dice_number):
total = sum(dice_numbers)
totals_frequencies[total] += 1
return totals_frequencies
def solution() -> float:
"""
Returns probability that Pyramidal Peter beats Cubic Colin
rounded to seven decimal places in the form 0.abcdefg
>>> solution()
0.5731441
"""
peter_totals_frequencies = total_frequency_distribution(
sides_number=4, dice_number=9
)
colin_totals_frequencies = total_frequency_distribution(
sides_number=6, dice_number=6
)
peter_wins_count = 0
min_peter_total = 9
max_peter_total = 4 * 9
min_colin_total = 6
for peter_total in range(min_peter_total, max_peter_total + 1):
peter_wins_count += peter_totals_frequencies[peter_total] * sum(
colin_totals_frequencies[min_colin_total:peter_total]
)
total_games_number = (4**9) * (6**6)
peter_win_probability = peter_wins_count / total_games_number
rounded_peter_win_probability = round(peter_win_probability, ndigits=7)
return rounded_peter_win_probability
if __name__ == "__main__":
print(f"{solution() = }")