N-Circular Tic-Tac-Toe
The game of 10-circular tic-tac-toe is played on the board below with 10 cells. Two players take turns placing naughts and crosses on the cells. The player who first places three consecutive symbols on the board wins.
Assuming optimal play, who has a winning strategy?
This problem was inspired by João Pedro Afonso 's solution to a different tic-tac-toe problem .
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
On the second player's first turn, he must place his symbol directly beside the first player's symbol, or else the first player can place two of his symbols in a row with empty spaces on either side and win. The optimal strategy for the second player on his first turn is to place his symbol directly beside the first player's symbol to avoid this from happening.
The optimal strategy for the first player is to remain in control of the game by placing his symbol in spots where he is able to place two of his symbols in a row, so that the second player must always respond by placing his symbol directly beside it.
Played with these two strategies, the game alternates with the first player attempting to get two in a row, and the second player blocking the attempt, until there is no more room left on the board to get three in a row for either player, after which the game will end in a tie.