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Even though this challenge is about times on clocks, the display on a calculator will help you to explore the patterns more easily than trying to write the numbers on paper. So grab a calculator and punch in some "times". A little hand mirror can help check for symmetry and reflections too.

Let us know what you find  by emailing! Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried. Teachers - you might like to send in a summary of your children's work.

Hurrah! In 2015 we had a solution come in from Jake at St George's C of E primary school
You have to have 1 at the start otherwise it won’t work.
Then when I started to think about it, I realised you could have 0 or 2 to start. You can’t have a number greater than 2 because it is a 24 hour clock.
If you used 8 (which has symmetry) you would have 18:81 and you can’t have 8 in the minutes as the highest number you can have is 59 in the minutes.
I then worked out you could have these times:

0 1:1 0
05:20's good
1 0:0 1
1 1 . 1 1
1 2:5 1
1 5:2 1
2 1:1 5
22:55  Jake

Thanks, that's a good answer, sorry your previous submission got lost in the airways.