## Solo noughts and crosses brainteaser

By David Shaw, 5 May 2022

**Difficulty: Tricky**

Mabel wanted to play noughts (O) and crosses (X), but she didn’t have anyone to play with. So she just took one go after another.

Somehow, Mabel put Xs in 6 of the 9 squares without making a line of 3 Xs.

Can you draw the board and work out which squares have Xs and which are empty?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

Another way to think about the problem is to reverse it. Can you put 3 Os on the board so that no matter where X goes, they can’t get a line of 3? If you can solve that puzzle, put Xs in all the empty spots and you should have your answer.

## Brainteaser answer

The solution is to leave empty the 3 boxes on one of the diagonals

* Image: CSIRO/David Shaw*

There are 9 squares on a noughts and crosses board. If Mabel put Xs in 6 of them, then 3 are empty.

There has to be one empty box in the top row, or it would be a line of 3. Similarly, there must be one empty in the second row, and one in the third row too. Since you only have 3 empty boxes, there is exactly one empty in each row.

That goes for the columns too – one empty in the first column, one in the second and one in the third.

You also need to block the diagonals. Leaving the centre empty solves that problem.

If you play around for a bit, you’ll find the solution is to leave empty the 3 boxes on one of the diagonals.

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