If ten points are on a unit square, one pair is at most $\sqrt2/3$ apart

Question

Ten points are placed in a unit square. Show that there is a pair of points at most $\sqrt2/3$ apart. I'm not sure how to proceed with this problem, and have not had any luck so far.

Answer 1

Hint: How would you go about dividing a square into nine pigeonholes so that two of the points would be in the same one?

If this really is Olympiad Training much better to take some time and solve it for yourself.

Answer 2

After receiving some tips, I now know how to proceed.The diagonals of the square are √2 long, so after dividing the initial square into 9 smaller squares, the diagonals are √2/3 long, and by the pigeon hole principle, the required results falls through