Question

Show that given any 9 points inside a square of side 1 we can always find 3 which form a triangle with area less than 1/8.

Answer 1

In order to prove this, let us first try to disprove it. Namely, let us choose 9 points within a square of side 1 which seem to be as far apart as possible (and thus will have the largest area).

Answer 2

I have drawn such a square with 9 points as spread out as possible above.