The game is really really hard (I never finished it without using a solver).
Adding a timer is not necessary, or eventually just to know how many steps it takes to finish the board.
But are you talking about a timer which ends the games when time is up or just a timer which says "it takes 126 steps to finish this board" ?
About the possible solution... Huh, actually I don't know if a board has a solution or not.
This is one thing on my todo list

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It seems that all symmetricals board are resolvable, so I can probably generate an half board and copy it to the second part of the board.
Do you have another idea? Some people says it's quite easy to generate well formed boards, but they don't say how
