Question

A web site was hit 300 times over a period of 15 days Show that over some period of 3 consecutive days, it was hit at least 60 times.

Answer 1

We will divide the 15 days in five periods of 3 consecutive days each.

Now to solve this we will use the pigeonhole principle.

This states that if (N+1) pigeons occupy N holes, then some hole must have at least 2 pigeons.

So, we have n=300 pigeons and k=5 holes.

`[(n)/(k) ]=[(300)/(5) ]`

Hence, there is a period of 3 consecutive days in which the website was hit at least 60 times.