MathDB

Let

m,n

be positive integers. An

n\times n

board has rows and columns numbered

1,2,\dots,n

from left to right and top to bottom, respectively. This board is colored with colors

r_1,r_2,\dots,r_m

such that the cell at the intersection of

i

th row and

j

th column is colored with

r_{i+j-1}

where indices are taken modulo

m

. After the board is colored, Ahmet wants to put

n

stones to the board so that each row and column has exactly one stone, also he wants to put the same amount of stones to each color. Find all pairs

(m,n)

for which he can accomplish his goal.
Proposed by Sena Başaran

Problem Statement