Posa used something mathematically called the pigeon hole principle in his proof. The principle is this: If you put n+ 1 items into n boxes, some boxes must contain at least 2 items. There are six-story dovecotes with four spaces on each floor, so there are 6×4=24 dovecotes in total. Now I have put 25 pigeons in it. You must see a pigeon cage. Two pigeons will be crowded together.

The principle of pigeon coop is so simple that children over 3 years old will understand it.

However, this principle has a very important application in mathematics.

19th century, a mathematician named Dirichlet (1805- 1859) skillfully used the pigeon-cage principle to solve problems in the study of number theory. Later, the German mathematician Min Guski (Minkowski1864-1909) also obtained some results by using this principle.

At the beginning of the 20th century, Toure (A. Thue 1863- 1922) skillfully solved the problem of rational number solution of indefinite equation by using pigeon cage principle without knowing the work of Dirichlet and Min Guski, and 12 papers used this principle.

Later, Siegel (C.L.Siegel, 1896-? ) We use Toure's results to find the Siegen Lemma, which is the most basic and necessary tool to study transcendental numbers.

Therefore, readers should not underestimate this seemingly simple principle. If you are good at using it, it can help you solve some math problems.