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TOT 343 1992 Autumn A J1 numbers in nxn table

Source:

June 10, 2024
combinatorics

Problem Statement

Numbers in an nn by nn table may be changed by adding 11 to each number on an arbitrary closed non-selfintersecting “rook path” (a broken line with segments parallel to the borders of the table). Originally 11’s stand on one of the diagonals, and $0S’s in the other cells of the table. Can one get (after several transformations) a table in which all numbers are equal to each other? (A “rook path” contains all cells through which it passes.)
(AA Egorov)