TOT 343 1992 Autumn A J1 numbers in nxn table
Source:
June 10, 2024
combinatorics
Problem Statement
Numbers in an by table may be changed by adding to each number on an arbitrary closed non-selfintersecting “rook path” (a broken line with segments parallel to the borders of the table). Originally ’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)