Python/project_euler/problem_01/sol2.py

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"""
2018-10-19 12:48:28 +00:00
Problem Statement:
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 N.
"""
def solution(n: int = 1000) -> int:
"""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
"""
sum = 0
terms = (n - 1) // 3
sum += ((terms) * (6 + (terms - 1) * 3)) // 2 # sum of an A.P.
terms = (n - 1) // 5
sum += ((terms) * (10 + (terms - 1) * 5)) // 2
terms = (n - 1) // 15
sum -= ((terms) * (30 + (terms - 1) * 15)) // 2
return sum
if __name__ == "__main__":
print(solution(int(input().strip())))