Showing that a website was hit at least $60$ times over a period of $3$ consecutive days A website was hit $300$ times over a $15$ day period. I must show that it was hit at least $60$ times over some period of $3$ consecutive days.
I was thinking that it would be best to solve this problem by contradiction and set up three day sections with $59$ total hits, but couldn't get anywhere with this method.
Can anyone help me with this?
Thanks!
 A: Problems like this can be handled by the Pigeonhole Principle.  This is one of my favorite tools in mathematics because of its usefulness and its intuitiveness.  The Pigeonhole Principle states that if you have $m$ pigeons and $n$ boxes (or holes), and you place each pigeon in some box, then at least one box has at least $m/n$ pigeons inside it.  This can also be worded as follows:
Suppose that you have $n$ real numbers $x_1, \dots , x_n$.  Then
$$
x_1 + \dots + x_n = C \Longrightarrow x_i \geq \frac{C}{n} \quad \text{for some } i.
$$
Similarly, if one has $n$ positive real numbers $x_1, \dots , x_n$, then
$$
x_1 \cdot \dots \cdot x_n = C \Longrightarrow x_1 \geq \sqrt[n]{C} \quad \text{for some } i.
$$
The easiest proof of this is probably the proof of the contrapositive:


*

*If one is given $n$ integers $x_1 , \dots , x_n$, and each of them is less than $\frac{C}{n}$, then


$$
x_1 + \dots + x_n < C.
$$
A: Hint:
If the hits are $d_1, d_2, \dots, d_{15}$
and $y_1 = d_1 + d_2 + d_3$, $y_2 = d_4 + d_5 + d_6$, ..., $y_5 = d_{13}+d_{14} + d_{15}$.
Can you figure out something about the $y_i$?
