In mathematics, the pigeonhole principle states that if *n* items are to be sorted into *m* bins and *n* > *m*, then at least of the containers must contain more than one item.

A more quantified version states that for natural numbers *n*, *k*, and *m*, if there are *n* = *km* + 1 items and *m* bins, then at least one bin will contain *k* + 1 objects.

The pigeonhole principle serves as the premise for many other useful postulates, including:

- If
*n*objects are distributed into*n*bins so that no bin contains more than one object, then each bin contains exactly one object. - If
*n*objects are distributed into*n*bins so that no bin contains no objects, then each bin contains exactly one object. - If
*n*objects are distributed into*m*bins and*n*<*m*, then at least one bin will contain no objects.

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