Python/project_euler/problem_001/sol3.py

"""
Project Euler Problem 1: https://projecteuler.net/problem=1

Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.
"""


def solution(n: int = 1000) -> int:
    """
    This solution is based on the pattern that the successive numbers in the
    series follow: 0+3,+2,+1,+3,+1,+2,+3.
    Returns the sum of all the multiples of 3 or 5 below n.

    >>> solution(3)
    0
    >>> solution(4)
    3
    >>> solution(10)
    23
    >>> solution(600)
    83700
    """

    total = 0
    num = 0
    while 1:
        num += 3
        if num >= n:
            break
        total += num
        num += 2
        if num >= n:
            break
        total += num
        num += 1
        if num >= n:
            break
        total += num
        num += 3
        if num >= n:
            break
        total += num
        num += 1
        if num >= n:
            break
        total += num
        num += 2
        if num >= n:
            break
        total += num
        num += 3
        if num >= n:
            break
        total += num
    return total


if __name__ == "__main__":
    print(f"{solution() = }")