Pigeon cage principle, also known as pigeon hole principle, is a basic principle of combinatorial mathematics. It was first put forward by the German mathematician Dirichlet, so it is also called Dirichlet principle. It is the content in Unit 5 of Mathematics Wide Angle, a sixth-grade mathematics book published by People's Education Press. By studying the pigeon nest problem, we can cultivate good logical thinking ability.
The pigeon's nest problem is an interesting mathematical problem closely related to life. Whether through experimental operation or drawing cartoons, it is not difficult for us to find that "there are always at least a few objects in a drawer" as soon as possible. First, we need to put the objects in different drawers as evenly as possible, and then divide the remaining objects into equal parts and put them in different drawers. There is a way to solve this kind of problem, and the key is to find out the number of objects and drawers.
An example of pigeon nest problem
For example, "put three apples in two drawers, so no matter how you put them, at least there are not less than two apples in 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.
When solving this kind of pigeon coop principle (pigeon coop problem), we should consider the worst case and analyze it from the worst case. The best case is to put all three apples in the same drawer, which is easy to achieve the goal. We should consider the worst case (average placement is the worst case), and put three apples in two drawers on average, with an average of 1 apple in each drawer, which is 1 apple more. No matter which drawer this 1 apple is put in, there are two apples in this drawer.