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numbers 0,1,-1 in 2nx2n board (VII Soros Olympiad 2000-01 R1 8.10)

Source:

July 27, 2021
combinatorics

Problem Statement

Place in the cells the boards measuring: a) 2×22 \times 2, b) 4×44 \times 4, c) 2n×2n2n \times 2n, numbers 00, 11 and 1-1 so that in each case all the sums of numbers in rows and columns are different.