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Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

Ten Green Bottles

Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?

Two Clocks

Age 7 to 11
Challenge Level

This problem needed a great deal of logical thinking. Excellent solutions were sent in by Zartasha from St Mary's C of E High School, Bryan from The British School of Guangzhou, Aporva from Brackensdale Junior and James B, James H, Jack W and Jack H from Tunbury Primary School. Remember that we like to hear the reasons for your answers, not just the answers.

The group of boys from Tunbury wrote:

Clock B is showing midday because midday is $12$ o'clock and the hand is pointing at $12$.
Clock D is showing the time when Sam gets up. Sam gets up at $7.20$ am (or thereabouts, perhaps $7.15$ am) because the other clocks would make him too late for school.
A shows when he goes to school because D is when you get up and get ready and $8.30$ am is roughly the time that you go to school. The other times are too early or too late.
Clock C shows that Sam turns out his light at $9.40$ pm (again, some of you thought this might be $9.45$ pm which is fine) .

Julie ran home from school on Friday because it took her $30$ minutes .
She stopped to buy some sweets on Monday because she got home at $10$ past $4$.
Julie stayed at school to practise with the band on Thursday because she got home at $10$ to $5$.
She stayed to play with Sam on Tuesday because she got home at $25$ to $5$.
Her teacher held the class in on Wednesday because she got home at $5$ past $4$.

Bryan from The British School of Guangzhou also sent in a clearly-reasoned solution for Julie's clock:

Monday the time is 4.10pm, buying sweets in the shop doesn't take a long time and it only takes $5$-$10$ minutes so she reached home at 4.10pm.
Tuesday the time is 4.35pm, she played with Sam for $30$ minutes and she might spend an extra 5 minutes getting home.
Wednesday the time is 4.05pm, her teacher kept the class for $5$ mins and she reached home at 4.05pm, but if she hadn't stayed she would have reached home at 4.00pm.
Thursday the time is 4.50pm, she practised with the band for about $45$-$50$ minutes so she got home at 4.50pm.
Friday the time is 4.00pm, it was raining so she hurried straight home and she did nothing in school so she might have got home in $30$ minutes.

Well done all of you!