Most Project Euler questions revolve around mathematical insight. This particular question has an O(1) solution!
A hint to point you in the right direction is to consider “triangle numbers”, or the 3rd line of Pascal’s triangle. The sum of all the numbers between 0 and 100 can be thought of as (0 + 100) + (1 + 99) + (2 + 98) + (3 + 97) … + (49 + 51) + 50. Using this sort of procedure, you can find the sum of any sequence of whole numbers from 0 to n by this equation:
(n^2)/2 + n/2, which is the same as n(n + 1) / 2
Can you think of a way to find the sum of all the numbers from 0 to n that are divisible by 3? Or the numbers divisible by 5? Or 15?
