MathDB
(n+1)^2 points inside a n x n square. Looks classical.

Source: 1st Romanian Master in Mathematics (RMIM) 2008, Bucharest, Problem 4

February 9, 2008
geometrypigeonhole principleperimetercombinatorial geometrycombinatorics proposedcombinatorics

Problem Statement

Consider a square of sidelength n n and (n\plus{}1)^2 interior points. Prove that we can choose 3 3 of these points so that they determine a triangle (eventually degenerated) of area at most 12 \frac12.