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

Answer:

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.

$[\frac{n}{k} ]=[\frac{300}{5} ]$

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