IMO Shortlist 2016 problem C4


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3. listopada 2019.
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Find all integers n for which each cell of n \times n table can be filled with one of the letters I,M and O in such a way that: in each row and each column, one third of the entries are I, one third are M and one third are O; and in any diagonal, if the number of entries on the diagonal is a multiple of three, then one third of the entries are I, one third are M and one third are O. Note. The rows and columns of an n \times n table are each labelled 1 to n in a natural order. Thus each cell corresponds to a pair of positive integer (i,j) with 1 \le i,j \le n. For n>1, the table has 4n-2 diagonals of two types. A diagonal of first type consists all cells (i,j) for which i+j is a constant, and the diagonal of this second type consists all cells (i,j) for which i-j is constant.

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf