Let the grid consist of r rows and k columns. Two players take turns moving a piece to an adjacent square (no diagonal moves). Once a square has been visited it cannot be visited again. The piece starts in the top left square, this square can therefore not be visited again. The loser is the player that does not have a legal move to make, as an example take a 2x1 grid, player 1 moves to the second square, and player 2 does not have a legal move, which means he loses. Is there a winning strategy, and what is it?
Obviously since draws are impossible, and this is a combinatorial game, there is a winning strategy. I firstly tried to imagine the game as an unary game of Nim with r*k piles. But this does not accurately represent the game. (Maybe I could do something with bogus-nim, but I'm not very good at that). I secondly tried to play against an RNG, trying to mirror their moves, if they vertically I move horizontally within reason of course, but that did not yield anything.
Does anyone have a hint? I don't want to be bold and ask for a very leading hint, but at this point I don't know what to do.
Obviously since draws are impossible, and this is a combinatorial game, there is a winning strategy. I firstly tried to imagine the game as an unary game of Nim with r*k piles. But this does not accurately represent the game. (Maybe I could do something with bogus-nim, but I'm not very good at that). I secondly tried to play against an RNG, trying to mirror their moves, if they vertically I move horizontally within reason of course, but that did not yield anything.
Does anyone have a hint? I don't want to be bold and ask for a very leading hint, but at this point I don't know what to do.