# Nimble

I don’t think anyone can beat this as a two-player mathematical game that’s so easy to use and so rich in development.

Write down the numbers from 1 to 9.

When it is your turn to play you MUST cross out the highest number in the line and you MAY cross out the next highest as well.

So here’s my first play (I’m red):

And here’s my opponent’s:

And my next play:

Play continues like this until one player wins by crossing out number 1.

Green wins!  Curses – I must do better next time.

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Children soon realise that if you can leave your opponent with just 1, 2, 3 remaining you’ve won the game.

However, it takes further insight to realise that …

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However, it takes further insight to realise that leaving someone with 1, 2, 3 isn’t just a matter of luck, because there’s actually an earlier position which will ensure you’re the person who does this.

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Yes, if you can make sure you leave your opponent with 1, 2, 3, 4, 5, 6 then they can’t prevent you – try it for yourself – from leaving 1, 2, 3 next turn.  So not only is 1, 2, 3 a winning position but so is 1, 2, 3, 4, 5, 6.  and of course there’s an earlier position that makes sure you leave your opponent with 1, 2, 3, 4, 5, 6.

So make sure you let them play first!

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So if you know your x3 table you can make sure you’re an expert at this game, but there are oodles of variations to try.  You can play with a different starting number – if you start with 1 to 10 do you want to play first or second?

Or change the rule so that you have three choices – crossing out the highest; or the highest and the next highest; or the highest, second highest, and the next highest?  (i.e. you can cross out one, two, or three numbers.)

And you can play with counters.

How does it affect things if the player who crosses out the final number loses the game?