# Pigeon-hole Principle

Although only a few questions have been asked from this concept so far in CAT, which is also true for some of the arithmetic topics like Profit and Loss; Calendar etc., the importance of this topic lies in the fact that this concept is purely logical and having a good practice over this concept gives a logical edge over others.

The concept is that if we put (N + 1) or more pigeons in N holes (nests), then at least one hole will be there which will have 2 or more pigeons.

Example
What is the minimum number of people in any group of five people who have an identical number of friends within the group, provided if A is a friend of B, then B is also a friend of A?
Solution
Since there are five persons in the group, so possible number of friends is 0, 1, 2, 3, 4. It seems here that everybody is having a different number of friends, so the answer is zero. But anybody having four friends ensures that nobody is having 0 friends. So, at least two persons must have the same number of friends.