Pigeonhole principle

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Start: The school has 400 students. Prove that a…

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12 puzzles in this collection

The school has 400 students. Prove that at least two of them were born on the sa

There are 40 students in the class. Is there a month in the year in which at lea

There are 30 students in the class. In the dictation, Vova made 13 mistakes, the

Of any three integers, you can choose two whose sum is even. Prove it.

Among any six integers, there are two numbers whose difference is a multiple of

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Pigeonhole Principle (Dirichlet's principle) is a simple, intuitive, and often useful method for proving statements about a finite set. This principle is often used in discrete mathematics, where it establishes a connect…

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Pigeonhole Principle (Dirichlet's principle) is a simple, intuitive, and often useful method for proving statements about a finite set. This principle is often used in discrete mathematics, where it establishes a connection between objects (“rabbits”) and containers (“cells”) when certain conditions are met. ‍

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The school has 400 students. Prove that at least two of them were born on the sa

There are 40 students in the class. Is there a month in the year in which at lea

There are 30 students in the class. In the dictation, Vova made 13 mistakes, the

Of any three integers, you can choose two whose sum is even. Prove it.

Among any six integers, there are two numbers whose difference is a multiple of

Prove that from any n + 1 integers you can choose two numbers whose difference i

Given 12 different two-digit numbers. Prove that you can choose two numbers from

From any hundred integers, can you choose two numbers whose sum is a multiple of

Are there a) fifty; b) more than fifty different two-digit numbers, the sum of n

Of any a) 51; b) 52 integers, can you choose two numbers whose sum or difference

There are 44 queens on the chessboard. Prove that each of them beats some other

Exact Science - Problem of The Day - 27