Question

If 5 tennis balls are put into 4 boxes, use the Pigeonhole principle to show that at least one box will contain 2 tennis balls

Answer 1

If 5 tennis balls are put into 4 boxes, with 5 tennis balls > 4 boxes, then at least one box will contain more than 1 tennis ball.

Explanation:

Answer 2

Explanation:

Well one of the first things you could do is put all 5 into one box. That means that that box contains at least 2 tennis balls.

Next being given to experiment, you put 2 balls in 1 box and 3 in another and the condition of 1 box containing at least 2 balls is still met.

So you do the best thing you can. You take 4 balls and put one in each box. So far you have not met the condition of the problem.

But you have one ball in your hand. Wherever you put the tennis ball, it must be in one of the boxes. That will meet the condition of the problem. One box has to have 2 balls in it.