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Stop the Clock

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This is a game for two players. You can use the interactivity below, or you could print off a page of blank clock faces in Word or as a pdf .

Set the time on the clock to $6$ o'clock to start the game.
Decide who will go first (player $1$) and who will go second (player $2$).
Take it in turns to choose to move the hands of the clock on by $\frac{1}{2}$ hour or by $1$ hour. For example, player $1$ could choose $\frac{1}{2}$ hour, so the clock hands move to 6.30, then player $2$ might choose $1$ hour, moving the clock hands to 7.30 ... etc.
The winner is the player who moves the hands exactly onto $12$ o'clock.

Can you work out a winning strategy so that you can always beat your opponent?

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