Prove that if you choose 11 integers then at least two of th

Prove that if you choose 11 integers, then at least two of them will have the same unit digit.

Solution

Answer:

There are 11 integers (pigeon) and 10 unit digits (pigeon holes).

Now by pigeonhole principle, there must be atleast 11 integers with the same unit digit.

Pigeonhole Principle: Suppose you have k pigeonholes and n pigeons to be placed in them. If n > k (# pigeons > # pigeonholes) then at least one pigeonhole contains at least two pigeons