### Times

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?

# Weekly Problem 42 - 2009

##### Stage: 2 and 3 Short Challenge Level:

The only digits which appear the same when reflected are $0$, $1$, $3$ and $8$, so we want to find the number of times the display on the clock is made up of these digits.

The first digit can be $0$ or $1$, the second digit can be $0$, $1$, $3$ or $8$, the third digit can be $0$, $1$ or $3$ and the fourth digit can be $0$, $1$, $3$ or $8$. Therefore there are $2\times 4\times 3\times 4=96$ different possible displays that are the same when reflected.

This problem is taken from the UKMT Mathematical Challenges.

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