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Times

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Clock Hands

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

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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: Challenge Level:1

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!