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.
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?