squares and the family
Source: Indonesia IMO 2007 TST, Stage 2, Test 4, Problem 4
November 15, 2009
combinatorics proposedcombinatorics
Problem Statement
Let be a finite family of squares on a plane such that every point on that plane is contained in at most squares in . Prove that can be divided into 4(k\minus{}1)\plus{}1 sub-family such that in each sub-family, each pair of squares are disjoint.