Choose 38 different natural numbers less than 1000, Prove among these there exists at least two whose difference is at most 26. Choose any 38 different natural numbers less than 1000.
Prove that among the selected numbers there exists at least two whose difference is at most 26.
I think I need to use pigeon hole principle, not sure where to even begin.

Pigeonhole-principle is a good idea.
Hint: Think about partitioning $\{1,2,\ldots,999\}$ into subsets $\{1,2,\ldots,27\}$, $\{28,29,\ldots, 54\}$, $\{55,56,\ldots,81\}$, ..., $\{\ldots,998,999\}$ of size $27$ each.
