Pigeon hole principle is also called pigeon nest principle. Pigeon hole principle was first used by Dirichlet, a German mathematician in19th century, to solve mathematical problems, so it is also called Dirichlet principle.

Principle 1: put m objects into n empty drawers at will (m > n, where n is a non-zero natural number), then there must be at least two objects in one drawer.

Principle 2: Put more than kn objects into n empty drawers at will (k is a positive integer), then there must be at least (k+ 1) objects in one drawer.

Principle 3: If an infinite number of elements are divided into n sets, at least one set contains an infinite number of elements.

In this kind of problem, it is only necessary to determine the existence of an object (or person), without pointing out which object (or person) it is, and without explaining how to find out the existing object (or person).

The current primary school textbooks only arrange the teaching of pigeon nest principle 1 and 2.

Second, the use of pigeon coop principle to solve the problem steps

Step 1: Analyze the meaning of the question. Distinguish what is "thing" and what is "drawer", that is, what is "thing to be divided" and what is "drawer".

Step 2: Make drawers. This is a key step, and this step is how to design drawers. According to the conditions and conclusions of the topic, combined with relevant mathematical knowledge, and mastering the most basic quantitative relationship, the drawer and its number needed to solve the problem are designed and determined, paving the way for the use of drawers.

Step 3: Apply the principle. Observe the problem-setting conditions, combine the second step, and properly apply various principles or comprehensively apply several principles in order to solve the problem.

Three, understand the principle of filing should pay attention to several points.

(1) The pigeon hole principle is to discuss the relationship between articles and drawers, and it is required that the number of articles be greater than the number of drawers or multiple of the number of drawers. As for how much, it doesn't matter.

(2) "Arbitrary placement" refers to the method of placing items in drawers without restriction, and it is not stipulated that every drawer should be placed with items, that is, some drawers can be empty, and the number of items placed in each drawer is not limited.

(3) The pigeon hole principle can only be used to solve the problem of existence, and "at least one" means existence. There may be multiple drawers that meet the requirements, but it is enough to ensure that only one drawer meets the requirements.

(4) Put the article A into n drawers. If a \ n = m ... b ... b, where b is a natural number, it can be obtained from pigeon's nest principle 2, and the number of articles in at least one drawer is not less than (m+ 1).