# Stop the Clock

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?

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?

A number of pupils from Mortimer School in England sent in their solutions.

Here are their comments:

Alice and Oliver:

When your partner is doing 1/2 an hour you should do a 1 hour.

Aaron and Mustafa:

Get the clock on to half past ten and then try and make him use half an hour and you use 1 hour so it goes on to 12 o'clock.

What would happen if your partner didn't use half an hour? Could you still win?

Harry and Gabe:

I pressed 1 hour when it was 11

Luke and Eve:

We think that you have to press 5 hours and 2 half hours for player 1 to win the game and 4 hours and 3 half hours for player 2 to win the game.

Dylan and Jacob:

We wrote that we did 1 hours and half an hour.

Thank you very much for these contributions. The difficulty is to find a way of winning that ALWAYS works.

Rhys from St. Michael's on the Mount in Bristol, England, sent in this email:

With this strategy if you go second you are guaranteed to win.

The aim is to get to 7.30, then 9.00, then 10.30 - after that you have won.

If player one goes to 6.30 you would go 1 hour to 7.30.

If player 1 goes to 7.00 on their opening move you would then go half an hour to 7.30.

That is a fantastic strategy, Rhys. I wonder if anyone can explain why it works?

### Why play this game?

### Possible approach

### Key questions

### Possible extension

### Possible support