def all_singles():
    return list(range(1, 21)) + [25]


def all_doubles():
    return [n * 2 for n in range(1, 21)] + [50]


def all_triples():
    return [n * 3 for n in range(1, 21)]


def euler_109():
    count = 0
    target_score = 100
    for first in all_doubles():
        # D
        if first < target_score:
            count += 1

        # D T
        for second in all_triples():
            if first + second < target_score:
                count += 1
        # D D
        for second in all_doubles():
            if first + second < target_score:
                count += 1
        # D S
        for second in all_singles():
            if first + second < target_score:
                count += 1

        # D T D
        for second in all_triples():
            for third in all_doubles():
                if first + second + third < target_score:
                    count += 1
        # D T S
        for second in all_triples():
            for third in all_singles():
                if first + second + third < target_score:
                    count += 1
        # D D S
        for second in all_doubles():
            for third in all_singles():
                if first + second + third < target_score:
                    count += 1

        # D T T
        for second in all_triples():
            for third in all_triples():
                if second >= third and first + second + third < target_score:
                    count += 1

        # D D
        for second in all_doubles():
            for third in all_doubles():
                if second >= third and first + second + third < target_score:
                    count += 1
        # S S
        for second in all_singles():
            for third in all_singles():
                if second >= third and first + second + third < target_score:
                    count += 1
    return count


if __name__ == "__main__":
    solution = euler_109()
    print("e109.py: " + str(solution))
    assert(solution == 38182)