Consider n2 unit squares in the xy plane centered at point (i,j) with integer coordinates, 1≤i≤n, 1≤j≤n. It is required to colour each unit square in such a way that whenever 1≤i<j≤n and 1≤k<l≤n, the three squares with centres at (i,k),(j,k),(j,l) have distinct colours. What is the least possible number of colours needed? combinatoricspigeonhole principle