Introduction to pigeon house principles

The concept of the pigeon house, also known as the drawer principle or the clay principle, is an important and basic mathematical principle. It can be used to solve various interesting problems, in addition, it is often surprising that many seemingly complicated or even difficult problems can be easily solved by using it.

Principle (1): if more than one element is divided into several sets in any definite way, there must be at least one set containing at least two elements. Principle (2): put more than m x n objects in N drawers, then there must be m + 1 or m + 1 objects in one drawer.