Pigeonhole principle for coprime numbers

Question

For a set of $n+1$ integers in $[2n]$, I would like to show that there always exist two coprime ones. This seems like a classic pigeonhole problem but I'm not sure what the pigeons or holds are.

Answer 1

One can use the pigeonhole principle to show that there are always two numbers next to each other. These must necessarily be coprime.