I remember reading a long time ago that there were lots of errors within the Trilogic game, but I have no idea how that game works and so wouldn't have noticed them myself and still don't know what they are.
I can understand how the game works, but I think you'd need to be a maths prodigy to be able to tell if it's being played right. I'm not.
From wiki:
When the Doctor is on move 905, he moves a piece so it counts as move 906. However, when the Celestial Toymaker asks the pieces to go to move 930, they only jump 21 times so it should be move 927.
In one spot of the Trilogic game, the smallest piece can be seen to be on top of the 5 piece. In order to get the minimum 1023 moves for the game, the smallest piece can never be put on top of another odd numbered piece – so the Doctor shouldn't be able to do it in 1023 moves.
Also, at 1000 moves, there are pieces on all three edges of the board. In the optimum solution of 1023 moves, one of the edges should be blank at 1000 moves. I'd never have known, either.