darts problem

darts.py

from itertools import product

CLOSING_SCORE = 167

def possible_dart_shots():
    shots = []
    for k, multi in enumerate(['single', 'double', 'tripple']):
        for segment in range(1, 21):
            shots.append((multi, (k + 1) * segment))

    shots.append(('single', 25))
    shots.append(('double', 50))
    shots.append(('miss', 0))
    return shots

def clean_misses(shot_sequence):
    return tuple(s for s in shot_sequence if s != ('miss', 0))

def get_closing_sequence(shot_sequence):
    score = 0
    for n, s in enumerate(shot_sequence):
        score = score + s[1]
        if score == CLOSING_SCORE and s[0] == 'double':
            return shot_sequence[:n + 1]
    return None


closing_shots = set()

for shot_sequence in product(possible_dart_shots(), repeat=3):
    closing_sequence = get_closing_sequence(shot_sequence)
    if closing_sequence:
        closing_shots.add(clean_misses(closing_sequence))

print(len(closing_shots))