Calculation formula of pigeon hole principle

If m elements are put into n drawers, there will be at least [(m- 1)/n]+ 1 elements in one drawer.

A more general expression of pigeon coop principle is:

"Put things that exceed kn+ 1 into N empty drawers at will (k is a positive integer), then there must be at least k+ 1 in one drawer."

Using the above principle, it is easy to prove: "In any seven integers, the difference between at least two numbers of three is a multiple of three." Because there are only three possible remainders when any integer is divisible by 3: 0, 1 and 2, at least three of the seven integers are divisible by 3 to get the same remainders, that is, the difference between them is a multiple of 3.

Extended data:

Construction method of drawer:

The core of applying pigeon coop principle is to analyze clearly which is the object and which is the drawer. For example, there are 12 zodiac signs, so at least one of any 37 people has at least four zodiac signs.

At this time, the zodiac is regarded as a 12 drawer, so a drawer has 37/ 12, that is, the remainder of 3 is 1, and the integer is considered upward, so here it is 3+ 1=4 people, but here it should be noted that the remainder in front is 1, and what is added here is

So in the problem, one more object and one less drawer. For example, the above question belongs to 12, which is the corresponding drawer, and 37 people are the corresponding objects, because 37 is greater than 12.

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