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# Sweeping Hands

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### Times

### Clock Hands

### Ten Green Bottles

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Well done to those of you who sent in the correct answer to this problem. A lot of you explained your reasoning very carefully, but sadly we are unable to name you all here.

Cong from Aberdeen sent in this solution:In $10$ minutes, the minute hand will sweep $60$ $^\circ$ degrees, because in $5$ minutes the minute hand will sweep $360\div12$ = $30$ $^\circ$.

In $3$ hours, the hour hand will sweep $90$ $^\circ$ degrees, because in $1$ hour the hour hand will sweep $360\div12$ = $30$ $^\circ$ .

If the minute hand goes through $180$ $^\circ$, the hour hand will sweep $15$ $^\circ$. The reason is as follows:

When the minute hand goes through $180$ $^\circ$, it is half an hour. In $1$ hour the hour hand will sweep $360\div12$ = $30$ $^\circ$ and $30$ $^\circ$ $\div2$ = $15$ $^\circ$. So when the minute hand sweeps $180$ $^\circ$, the hour hand will turn $15$ $^\circ$.

Joshua from Sydney Grammar School had a slightly different approach to the second part of the problem:

In three hours, the hour hand will travel a quarter of a full revolution, which is $90$ $^\circ$.

For those of you who misread this question and calculated the number of degrees that the minute hand turned through, better luck next time!

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!

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

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?