The pigeonhole principle

You can place $n$ objects into $m$ groups, if there are more groups than objects.

​ If we distribute $n$ objects into $m$ groups ($n>m$), there will be at least one group in which there is more than one object. ​

You can always place pigeons in pigeonholes.

If two pigeons are in the same pigeonhole, then there are fewer pigeonholes than there are pigeons.