The drawer principle: Why can it be judged by the method of averaging the score, no matter how to pu

Drawer Principle In daily life, as long as people pay a little attention, it is not difficult to find some things with regularity. For example, if you put 10 apples in 9 drawers, then there must be two or more apples in one drawer. This is a simple principle that everyone understands, and it is known as the drawer principle or the pigeon cage principle (comparing a pigeon to an apple and a cage to a drawer).

The general form of the drawer principle is: if n+1 apples are placed in n drawers, then at least two or more apples are placed in at least one drawer.

Don't underestimate this simple principle, many interesting problems can be solved with the drawer principle. For example, 2 out of every 13 people must be born in the same month. It is only necessary to look at 13 people as apples and 12 months as drawers, so the drawer principle is concluded.

For example, in a square with a side length of 1, given any given 5 points, there must be 2 of them, and the distance between them will not be greater than 1 2To prove the problem, we only need to divide the square into 4 equal parts, so that the sides of the 4 small squares are all 1 2, and the distance between any two points in each small square is not greater than the diagonal length of the large square 1 2Think of 5 dots as apples and 4 small squares as drawers, and according to the drawer principle, there must be 2 dots in a small square, so the distance between these two dots is not greater than 1 2

If you look at the middle school competition book, the first part is about the principle of flexion. I'll give you an example. There are three apples, and now I'm going to put them in two stubs.

So is there at least one of the trumpets with an apple in it? It can also be understood by drawing. That's how the original truth came about.

1. The reason why the drawer principle highlights the idea of average score is because the drawer principle itself was invented on the basis of average score.

2. The drawer principle, also known as the pigeon's nest principle, is a basic principle of combinatorics, which was first explicitly put forward by the German mathematician Dirichlet, so it is also known as Dirichlet principle. One of the simple expressions is: if there are n cages and n+1 pigeons, and all the pigeons are kept in the cages, then at least one cage has at least 2 pigeons.

The other is: if there are n cages and kn+1 pigeons, and all the pigeons are kept in the pigeon cage, then at least one cage has at least k+1 pigeons.

The principle of drawers is simply as follows: if more than n items are placed in n drawers, the number of items in at least one drawer is not less than 2 (at least 2 items are in the same drawer). For example, if you buy 6 pieces (or 7 or 8 pieces) of sugar, you need to put it in 5 small sugar boxes, no matter how you put it, at least one box has at least 2 sugar in it.

Drawer principle 2: If more than m n items are placed in n drawers, the number of items in at least one drawer is not less than m+1 (at least m+1 items are in the same drawer).

There is also a reverse drawer principle, which is an inverse use of drawer principle 2, and pushes out m by no less than m+1.

The general steps to apply the drawer principle are:

1. Construct drawers according to the characteristics of the elements.

2. Put the elements in the drawer.

3. Use the drawer to solve the problem.

To put it simply, the drawer principle is to consider the worst-case scenario, and give you an example to understand.

There is a full deck of poker, and a maximum of how many cards are drawn to ensure that at least 6 cards of the same suit are guaranteed.

First of all, it is important to understand that a complete poker game has 1 king, 1 king, and 13 hearts and spades, squares, and clubs. To draw 6 cards of the same suit, consider the worst case, that is, clubs, squares, hearts, spades each draw 5 cards, and then draw 1 king and 1 small king, and then no matter how you draw, there will be 6 cards of the same suit if you draw another one. So draw up to 5+5+5+5+1+1+1+1=23 cards.

8th 100-86=14

The average score of 14 to the results of the previous exams (84) is drawn into two points, and 14 divided by 2 = 7There were 7 exams in the past, and this time it must be the 8th.