Pigeonhole principle proving that 2 children out of 15 received the same number of sweets, from 100

Question

Whilst I do understand this conceptually I do not know how to formally provde this. 100 sweets were distributed between 15 children. Use the pigeonhole principle to prove that 2 children received the same number of sweets.

Answer 1

Hint

This is coming from the fact that $0+1+2+3 +\dots +14=\frac{14*15}{2}=105 >100$.

So if you want to distribute at most $100$ candies, you need to repete at least one of the number below or equal to $14$ at least twice.