At each move a player chooses an "O" and turns it into an "X". At the same time
this player may, if he so wishes, change a letter in any other square to the left from
the first one. In the left square, the player is allowed to turn "O" into "X" and also "X" into "O".
To perform a move, the player should first click under the square he plans to change. After selecting
1 or 2 squares, click on the "Make Move" button. If you plan to change a single square (an "O" into an "X") you
may click on that square directly. This is kind of a shortcut with which one should be cautious. You
can't undo your moves. The player to make the last move wins.
In the original version, players turn turtles upside down and back to their feet. Not having
any aptitude for painting, I settled on the TicTacToe symbols to present the two possible states of each square.
The game is a Nim in disguise, Nim with eleven rows of lengths
1,2,3,.,and 11. Each square corresponds to one row. "X" in a row indicates that a row is empty while "O" means
that the row is full of check marks. Changing "O" into "X" is the same as removing
a whole row of check marks. If you wish to remove m check marks from a row that has n>m
of them, change the square number n and then change the square number n-m to the left. It does not matter whether
at this point m contained "O" or "X".
E.R.Berlekamp, J.H.Conway, R.K.Guy, Winning Ways for Your Mathematical Plays, v1, A K Peters, 2001.
E.R.Berlekamp, J.H.Conway, R.K.Guy, Winning Ways for Your Mathematical Plays, v2, Academic Press, 1982.