You're given $51$ natural numbers between $[1,100]$. Show that there are two of these numbers whose sum is $101$.

Question

You're given $51$ natural numbers between $[1,100]$. Show that there are two of these numbers whose sum is $101$.

This seems to be an application of the pigeonhole principle? I started considering different sets as the boxes, but this didn't quite lead anywhere. How should I approach this kind of problem?

Answer 1

Hint: Consider pairs $(1,100),(2,99),\cdots ,(50,51).$