2016 IMO Problems/Problem 2
Find all integers for which each cell of table can be filled with one of the letters and in such a way that: [LIST] [*] in each row and each column, one third of the entries are , one third are and one third are ; and [/*] [*]in any diagonal, if the number of entries on the diagonal is a multiple of three, then one third of the entries are , one third are and one third are .[/*] [/LIST] [b]Note.[/b] The rows and columns of an table are each labelled to in a natural order. Thus each cell corresponds to a pair of positive integer with . For , the table has diagonals of two types. A diagonal of first type consists all cells for which is a constant, and the diagonal of this second type consists all cells for which is constant.