Add solution to Project Euler problem 205

project_euler/problem_205/sol1.py

@@ -0,0 +1,73 @@
+"""
+Project Euler 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 Pete beats Cubic Colin? Give your answer rounded
+to seven decimal places in the form 0.abcdefg
+"""
+
+from itertools import product
+
+
+def probability_of_sums(
+    dice_min: int = 1, dice_max: int = 6, dice_number: int = 6
+) -> (list, list):
+    """
+    Returns the list of possible sums and their probabilities of dice_number dices with
+    numbers from dice_min to dice_max
+    """
+    sums = []
+    counter = []
+    for dices in product(range(dice_min, dice_max + 1), repeat=dice_number):
+        s = sum(dices)
+        if s not in sums:
+            sums.append(s)
+            counter.append(1)
+        else:
+            idx = sums.index(s)
+            counter[idx] += 1
+    total = sum(counter)
+    probability = [_t / total for _t in counter]
+    return sums, probability
+
+
+def solution():
+    """
+    Returns the probability of Peter winning in dice game with nine four-sided
+    dice (1, 2, 3, 4 points) against Colin who has six six-sided dice (1, 2, 3, 4, 5,
+    6). Winner of a match is who has more total points.
+    Algorithm calculates the possible point sums for each player and their
+    probabilities. Peter's probability to win is summed up from all the permutations
+    where he has more points than Colin.
+
+    >>> solution()
+    0.5731441
+    """
+    peter_wins = 0
+    colin_wins = 0
+    draw = 0
+    for s_peter, p_peter in zip(
+        *probability_of_sums(dice_min=1, dice_max=4, dice_number=9)
+    ):
+        for s_colin, p_colin in zip(
+            *probability_of_sums(dice_min=1, dice_max=6, dice_number=6)
+        ):
+            p_branch = p_peter * p_colin
+            if s_peter > s_colin:
+                peter_wins += p_branch
+            elif s_colin > s_peter:
+                colin_wins += p_branch
+            else:
+                draw += p_branch
+
+    return round(peter_wins, 7)
+
+
+if __name__ == "__main__":
+    print(solution())