# Filling a chessboard with -1, 0 and 1

You have a standard chessboard $(8\times8)$.
And you have a lot of numbers from the set $[-1, 0, 1]$.
You have to place one number in each square so that the sums on each row, column, and the two diagonals are different.

To clarify, they must all be unique, regardless of direction (not just different among rows or columns).

If you can do that, what's the strategy?
If not, why?

• We'have had this question before, but without the diagonal rule... Not sure if I can dig it up. May 9, 2016 at 17:47
• hey...why the downvote? what's wrong with my question? May 9, 2016 at 17:47
• @TimCouwelier You might be thinking of this one, but that was for an 11x11 board (the result was that it's impossible for odd side lengths).
– f''
May 9, 2016 at 17:51
• @f'' That's the one indeed. Good thing I was trying to confirm that before attempting to actually flag it as duplicate. I have to say, the added rule about the diagonals does make it rather trivial.. May 9, 2016 at 17:52
• @TimCouwelier The "primes and composites" version was also trivial, but it seems to have been better received...
– f''
May 9, 2016 at 17:54