Is it possible to construct a matrix with 5*5 cells, where the value in each cell is taken from the set {-2,-1,0,1,2}, such that all of the 12 sums of the cells in each row/column/main diagonal have different values (5 sums of matrix's rows, 5 sums of the matrix's columns, and 2 sums of the main diagonals)?


1 Answer 1


Assuming I haven't missed something, this appears to work

enter image description here

I started by just putting -2 in the top row. The sum is -10, so I made the first column sum to a different number -9. I repeated this pattern until the diagonal was completed. The sum of the diagonal (bottom left to top right) was -5, so I skipped -5 and continued with -4. The remaining few cells were trivial to select to have different numbers.

To assist in ensuring I didn't miss a number, I applied conditional formatting to the sum cells in Excel so that they would be highlighted red if a value was duplicated.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.