# Thread: please help me prove this problem.

1. ## please help me prove this problem.

there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

thank you.

2. ## Re: please help me prove this problem. Originally Posted by rcs there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

thank you.
Do you mean "there are five points inside a square of side two length 2"?
Your statement as is makes no sense at all.

3. ## Re: please help me prove this problem. Originally Posted by rcs there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

thank you.
Seems like a pidgeon hole. You can hide 4.

4. ## Re: please help me prove this problem. Originally Posted by rcs there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.
Lets assume that this concerns a square that is $2\times 2$.
Suppose we have four smaller squares that are each $1\times 1$. The length of the diagonal of any one the the smaller squares is $\sqrt2$.
Question: Is it possible to use the four smaller squares to completely cover the larger square?