How Many Times?
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!
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