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