MathDB
RMO 2017 P4

Source: RMO 2017 P4

October 8, 2017
combinatoricspigeonhole principle

Problem Statement

Consider n2n^2 unit squares in the xyxy plane centered at point (i,j)(i,j) with integer coordinates, 1≤i≤n1 \leq i \leq n, 1≤j≤n1 \leq j \leq n. It is required to colour each unit square in such a way that whenever 1≤i<j≤n1 \leq i < j \leq n and 1≤k<l≤n1 \leq k < l \leq n, the three squares with centres at (i,k),(j,k),(j,l)(i,k),(j,k),(j,l) have distinct colours. What is the least possible number of colours needed?
Back to ProblemsView on AoPS