- 11 Jul '11 15:47 / 1 editIt's definitely impossible to solve. Although I'm still working on a proof.

My conjecture is that it'll be solvable for an nxn grid where the number of dominoes needed to ensure we don't have any possible slices divided by the total grid is less than 1/2

(2x(n-1))/nxn < 1/2

And it's easily solved for n=8,10 etc.

something about needing enough spaces to fill in the rest of the board due to the facts that all the dominoes need to be in pairs. - 11 Jul '11 16:42Actually that kind of is my prove. Every domino placed will need a pair (otherwise you won't be able to fill the board) and there just aren't enough squares on a 6x6 board to allow enough pieces to stop all possible slices AND for each piece to have a pair.

Kind of an informal proof, but the best I can come up with. - 11 Jul '11 19:55

I think that is essentially right! Nice one*Originally posted by VelvetEars***Actually that kind of is my prove. Every domino placed will need a pair (otherwise you won't be able to fill the board) and there just aren't enough squares on a 6x6 board to allow enough pieces to stop all possible slices AND for each piece to have a pair.**

Kind of an informal proof, but the best I can come up with. - 24 Jul '11 22:18Basically the only way I can see to prove it, is to prove the equivalent theorem that in placing dominoes, each must have a pair (another domino in the same configuration on the same row or column) as otherwise it'll be impossible to fill the board completely without leaving gaps.

However, how to prove that eludes me, it looks a bit like a parity problem in group theory, however it's been a couple of years since I studied group theory so I'm not sure I can prove it.

Then again I could be going in completely the wrong direction here and I look forward to being proved wrong.