$15$ students collected $100$ flowers. Prove that at least two of them have collected the same number of flowers.

Question

Question above. I'm really not sure how to proceed.

$15$ students collected $100$ flowers. Prove that at least two of them have collected the same number of flowers.

Answer 1

Let's say each one of them collected different number of flowers. In that case total number of flowers must be at least

$$0+1+2+3+...+14=105$$

And now $105>100$

It shows at least two of them collected same number of flowers.

Or

if everyone is collected at least one flower then

$$1+2+3+...+15=120$$

And now $120>100$