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2021 IIMC keystage3-IWYMIC team Question 1

xIMC · 2021 IIMC keystage3-IWYMIC team

Question 1

Consider the ‘I’ shaped diagram below:

Question illustration

Each square is filled with exactly one number from the following eight numbers $-1,-1,-1,0,0,1,1,1$ such that the sum of the numbers in each of the rows, column and four corners are all the same. How many ways are there to fill the diagram?

Question illustration