September 20, 2024


I recently discovered an interesting variant of zeros and crosses. (Tic-tac-toe for US readers.) Games are played exactly as normal with the following twist:

Players can place an X or an O each time.

That’s right, you can swing both ways. A player can play X at one time and O at the next, or vice versa, or stick with the same symbol. On each path it is up to the player to decide. As usual, the first player to get a line of three O’s or X’s wins.

Normal zero points and crossings get boring quickly because you can’t guarantee a win and two skilled players will always play to a draw. (The person who goes first can guarantee a win if they start in a corner and the second player doesn’t go in the middle.)

But with ‘naughty’ noughts and crosses, the player who goes first can always win. Today’s puzzle is to work out how this is done.

I’d recommend playing the game a few times to get the feel of it – it revives a tired old classic. But if there are no eight-year-olds on hand, here is a sample game between a red and a blue player.

Player 1 places an X. Player 2 also decides to place an X, but only has two safe spots.
Player 1 wants to play an X and has only one safe spot. Player 2 cannot place an X without losing, so now places an O.
Player 1 must also place an O and has a choice of three safe spaces. Player 2 must again place an O in one of the remaining two safe spots.
Player 1 still cannot place a safe X, so must place an O. Player 2 now has no safe O’s, and places an X to force a tie.

I’ll be back at 5pm UK with the solution. In the meantime, please discuss other variants of classic games. Or stock cubes.

PLEASE NO SPOILERS

I read about naughty nuts and crosses in a curious new book called John Driscoll A hen and a half, intriguing riddles, perplexing paradoxes, perplexing conjectures and challenging puzzles. Readers of this column will find it full of entertaining material.

If you are curious about the title, A Hen and a Half, it is from a famous puzzle that I once wrote about this.

I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.

my new book Think twice: Solve the simple puzzles (almost) everyone gets wrong (Square Peg, £12.99), is out on 5 September. To support the Guardian and Observer, order your copy from guardianbookshop.com. Delivery charges may apply.



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