$6967$ notes labelled $1,2,3,4,…,6967$,choose $K$ notes at random,the smallest number $K$ to ensure that two notes labelled by consecutive numbers

Question

There are $6967$ notes labelled $1,2,3,4,…,6967$. If you choose $K$ notes at random, what is the smallest number $K$ that would guarantee that you pick two notes labelled by consecutive numbers? Use the pigeonhole principle to explain

I'm not quite sure in this question what the pigeons and pigeonholes are. If someone could explain that would be great

Answer 1

Picking all the odd numbers gives a maximal set without neighbours and $3484$ elements. Divide the set in $\{1,2\}$, $\{3,4\}$, ..., $\{6965,6966\}$, and $\{6967\}$; that's $3484$ pigeon holes, so if you pick $3485$ numbers at least one pigeon hole gets picked from twice.