Can you solve it? Naughty noughts and crosses | Mathematics

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

Players can place either an X or an O on each go.

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

Normal noughts and crosses gets boring fast because you cannot guarantee a win and two competent players will always draw. (The person going first can guarantee a win if they start in a corner and the second player doesn’t go in the middle.)

But with ‘naughty’ naughts and crosses, the player going 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 reinvigorates a tired old classic. But if there are no eight-year-old children at hand, here’s an example game between a red and a blue player.

Player 1 places an X. Player 2 decides also to place an X, but only has two safe places.
Player 1 wants to play an X and only has one safe place. 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 again must place an O in one of the remaining two safe places.
Player 1 still can’t place a safe X so must place an O. Player 2 now has no safe Os, and places an X to force a draw.

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

PLEASE NO SPOILERS

I read about naughty naughts and crosses in a quirky new book by John Driscoll called A Hen and a Half, Intriguing Conundrums, Confusing Paradoxes, Baffling 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 here.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like 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 September 5. To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.

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