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You could print off a sheet of blank clocks (Word document or pdf) to record the times you and your partner choose.
Play the game several times. What do you notice?
What happens if your opponent gets to 10.30? Why?
How can you make sure you get exactly on $12$ o'clock? What time would you leave on the clock so that you can get to 12.00 on your next go, after your opponent has been?
So, what time would you want the clock to say on the go before that?
How can you work out these "key times" that you must "land on" on your way to the target?