### 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?

# Watch the Clock

##### Stage: 2 Challenge Level:

This challenge caused a lot of hard thinking. Some took the time to be around 2.10 and others around 3.15 according to how they interpreted the question. Either way led to some careful working out. The amount the small hour hand moves led to slightly different suggested answers.

Hasa, Javeria and Sarah wrote:

First we estimated an answer. The answer must be between 2 and 3 on the clock. So it must be between 2:10 and 2:15. Then we worked out how many degrees each hand moves in 1 minute.

The minute hand moves $360\div60=6$ degrees per minute.
The hour hand moves $(360\div12)\div60=0.5$ degrees per minute.
If $T$ is the time in minutes after 2:00 then the minute hand has moved $6T$ degrees.
The hour hand has moved $60+0.5T$
When the hands are pointing in the same direction these must be equal
$6T=60+0.5T$
$5.5T=60$
$T=60\div5.5$
$= 120\div11$
$= 10$ min$+10\div11$ x $60$ sec
= $10$ min $55$ sec (to the nearest second) after 2:00

Isobel sent in her suggestion as:

I found out that roughly the answer was 3:17 am. I found this puzzle quite tricky. So I borrowed my mum's alarm clock and fiddled with the arms until I found the answer.