The Answer to the Question
is below this banner.
Here's the Solution to this Question
A 3cm by 3cm squre board are divided by nine 1cm by 1cm squares. Since there are 10 points, by the Pigeonhole Principle there is a 1cm by 1cm square that contains at least two points. Since the maximal distance between any two points in the square is equal to the length of a diagonal which is equal to for the 1cm by 1cm square, we conclude that two points must be at least cm apart.