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China Mathematical Olympiad 1992 problem3

Source: China Mathematical Olympiad 1992 problem3

September 30, 2013
combinatorics unsolvedcombinatorics

Problem Statement

Given a 9×99\times 9 grid, we assign either +1+1 or 1-1 to each square on the grid. We define an adjustment as follow: for each square on the grid, we make a product of all numbers of those squares which share a common side with the square (excluding itself).Then we have 8181 products. Next we replace all the squares’ values with their corresponding products. Determine if we can make all values in the grid equal to 11 through finite adjustments.