Summary of pigeon's nest problem and answering skills

The pigeon nest problem summary and answering skills are as follows:

First, the overview of pigeon coop problem.

1, pigeon nest problem generally requires that the number of elements in each set cannot exceed a given value.

2. Pigeons in the pigeon nest problem represent elements, and sets represent nests.

3. If the number of pigeons is greater than the number of nests multiplied by the maximum number of pigeons in each nest, there must be two pigeons in at least one nest.

Second, the pigeon's nest question answering skills

1, determine the number of pigeons and nests.

2. Determine the maximum number of pigeons in each nest.

3. Use the principle of multiplication to calculate the total number of schemes.

4. Calculate the number of unqualified schemes by subtraction principle.

5. Subtract the number of unqualified schemes from the total number of schemes to get the number of qualified schemes.

6. Generally, it is necessary to convert the number of programs that meet the requirements into proportions or percentages.

Principle of pigeon nest problem;

The pigeon nest problem is an important principle in combinatorial mathematics. It was first put forward by the German mathematician Dirichlet and applied to solving problems in number theory, so this principle is also called Dirichlet principle.

This paragraph is abstract and difficult to understand. In fact, it is often used in life, such as putting three apples in two drawers, so no matter how you put them, there are at least two apples in at least one drawer. The basic structure of pigeon nest principle (pigeon nest problem) is divided into three parts: the number of objects and the number of drawers (pigeon nest). There is always a drawer with at least a few items in it.