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For the game with a target of 23, and numbers 1, 2, 3 and 4 to choose from, Remi said:

You can work backwards from the end to see how you can always win.

If the computer lands on 22, 21, 20 or 19 then you can win, because you can choose 1, 2, 3 or 4.

If you land on 18, then the computer has to land on 19, 20, 21 or 22. So if you land on 18, you'll be able to win.

If the computer lands on 17, 16, 15 or 14 then you can land on 18 and then win.

If you land on 13, you force the computer to land on 14, 15, 16 or 17.

This happens every 5 numbers, because for any number from 1 to 4 that the computer chooses, you can choose your number so that they add up to 5.

The 'winning numbers' that you have to land on are 18, 13, 8 and 3. If you let the computer land on these numbers, then you will lose!

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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