Problem
COM-B1-M05-P011 Five Points in a Square
#11
★★☆☆☆ Level 2 of 5
In a square of side \(2\), \(5\) points are chosen. Prove that two are at distance at most \(\sqrt{2}\).
Divide the square into \(4\) unit squares.
After dividing into \(4\) unit squares, \(5\) points force two points into one small square. The distance between any two points in a unit square is at most its diagonal \(\sqrt{2}\).
Geometric pigeonhole.