Colored Points on a nxn Chessboard, finding a limit
Source: Turkish NMO 1998, 6. Problem
July 31, 2011
limitcombinatorics proposedcombinatorics
Problem Statement
Some of the vertices of unit squares of an chessboard are colored so that any ( ) square consisting of these unit squares has a colored point on at least one of its sides. Let denote the minimum number of colored points required to satisfy this condition. Prove that \underset{n\to \infty }{\mathop \lim }\,\frac{l(n)}{{{n}^{2}}}=\frac{2}{7}.