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An arrangement of non-zero numbers in a square.

Source: Tuymaada 2001, day 2, problem 2.

April 30, 2007
combinatorics proposedcombinatorics

Problem Statement

Non-zero numbers are arranged in n×nn \times n square (n>2n>2). Every number is exactly kk times less than the sum of all the other numbers in the same cross (i.e., 2n−22n-2 numbers written in the same row or column with this number). Find all possible kk.
Proposed by D. Rostovsky, A. Khrabrov, S. Berlov
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