11.4

Part of 1995 All-Russian Olympiad Regional Round

Problems(1)

squares intersection in the plane

Source: Russia 1995

there are some identical squares with sides parallel, in a plane. Among any

k+1

of them, there are two with a point in common. Prove they can be divided into

2k-1

sets, such that all the squares in one set aint pairwise disjoint.

inductioncombinatorics proposedcombinatorics