Nailing Paper Squares
Source: All-Russian MO 2000
December 30, 2012
combinatorics unsolvedcombinatorics
Problem Statement
Some paper squares of distinct colors are placed on a rectangular table, with sides parallel to the sides of the table. Suppose that for any squares of distinct colors, some two of them can be nailed on the table with only one nail. Prove that there is a color such that all squares of that color can be nailed with nails.