Problem

Source: Indonesia IMO 2007 TST, Stage 2, Test 4, Problem 4

Tags: combinatorics proposed, combinatorics



Let $ S$ be a finite family of squares on a plane such that every point on that plane is contained in at most $ k$ squares in $ S$. Prove that $ P$ can be divided into $ 4(k-1)+1$ sub-family such that in each sub-family, each pair of squares are disjoint.