MathDB
number of k which are n-squared

Source: ItaMO 2009, p6

February 23, 2012
geometryrectanglefunctioncombinatorics unsolvedcombinatorics

Problem Statement

A natural number kk is said nn-squared if by colouring the squares of a 2n×k2n \times k chessboard, in any manner, with nn different colours, we can find 44 separate unit squares of the same colour, the centers of which are vertices of a rectangle having sides parallel to the sides of the board. Determine, in function of nn, the smallest natural kk that is nn-squared.