### 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?

# How Many Times?

##### Stage: 2 Challenge Level:

Jay and Ben (Mile Cross Middle School) sent in a correct solution:

Between midnight and 7:00 we found ten

0:12

1:23

5:43

6:54

2:34

3:45

3:21

4:32

4:56

2:10



There are no times between 7:00 and midday .
We found two times between midday and midnight. These are 12:34 and 23:45.

Syed (Foxford School and Community College) agrees with this answer and makes a statement about why you don't get times containing a 7, 8, or 9 in the solution:

The largest the tens digit of the minute number can be is 5, so the largest unit of the hour number is 6 in order for the time to have consecutive digits.

George (Rosebank Primary School, Leeds) also solved this one and explained his thinking well.

Jason (Priory Middle School, Dunstable) took a different view of this problem. Instead of only looking at single digit numbers, he also looked for consecutive two-digit numbers. This is what he found:

 For midnight to 7am For 7am to midday For midday to midnight 1:23 10:11 12:13 23:22 2:34 11:12 13:14 22:21 3:45 11:10 14:15 21:20 4:56 15:16 20:19 2:10 16:17 19:18 3:21 17:18 18:17 4:32 18:19 17:16 5:43 19:20 16:15 6:54 20:21 15:14 21:22 14:13 22:23 13:12 23:24 12:11 0:23

Some interesting patterns here Jason!