Choose any 9 points on or within a unit square. Prove that there always exists 3 points such that triangle formed by them has area 1/3
Consider a equilateral triangle of total area 1. Suppose 7 points are chosen inside. Show that some 3 points form a triangle of area $\leq\frac 14$.
How small parallelograms are we guaranteed to get, when we select the two sides from different plane lattices?
This a shortened version (motivation from telecommunications stripped away) of a question I asked in MO in late May (no answers). I am mostly checking, if somebody has seen this or a related question ...
If any x points are elected out of a unit square, then some two of them are no farther than how many units apart?
If 5 points are randomly positioned in a unit square, no two points can be greater than square root of 2 divided by 2 apart; divide up the unit square into four squares, and, based on the pigeonhole ...