sol1.py

"""
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
"""

fromitertoolsimportproduct


deftotal_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)
fordice_numbersinproduct(faces_numbers, repeat=dice_number):
total=sum(dice_numbers)
totals_frequencies[total] +=1

returntotals_frequencies


defsolution() ->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
forpeter_totalinrange(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)

returnrounded_peter_win_probability


if__name__=="__main__":
print(f"{solution() =}")