How often in a 12 hour period does the sum of the digits on a digital clock equal 9?

Answer 1

To find out how often the sum of the digits on a digital clock equals 9 in a 12-hour period, we need to consider the possible combinations. The sum of the digits can be 9 in the following cases: 09:45, 10:35, and 12:24. Therefore, the sum of the digits equals 9 three times in a 12-hour period.

Answer 2

As you have not specified which 12 hour period, it has to be assumed that the clock displays am/pm times using hours 1-12 and not a 24 hour digital clock using the hours 0-23.

Also, the result will depend upon whether seconds are displayed or not:

• am/pm digital clock with no seconds displayed

There are 57 such times:

1:08 1:17 1:26 1:35 1:44 1:53 2:07 2:16 2:25 2:34 2:43 2:52 3:06 3:15 3:24 3:33 3:42 3:51 4:05 4:14 4:23 4:32 4:41 4:50 5:04 5:13 5:22 5:31 5:40 6:03 6:12 6:21 6:30 7:02 7:11 7:20 8:01 8:10 9:00 10:08 10:17 10:26 10:35 10:44 10:53 11:07 11:16 11:25 11:34 11:43 11:52 12:06 12:15 12:24 12:33 12:42 12:51

• am/pm digital clock with seconds displayed

There are 804 such times:

1:00:08 1:00:17 1:00:26 1:00:35 1:00:44 1:00:53 1:01:07 1:01:16 1:01:25 1:01:34 1:01:43 1:01:52 1:02:06 1:02:15 1:02:24 1:02:33 1:02:42 1:02:51 1:03:05 1:03:14 1:03:23 1:03:32 1:03:41 1:03:50 1:04:04 1:04:13 1:04:22 1:04:31 1:04:40 1:05:03 1:05:12 1:05:21 1:05:30 1:06:02 1:06:11 1:06:20 1:07:01 1:07:10 1:08:00 1:10:07 1:10:16 1:10:25 1:10:34 1:10:43 1:10:52 1:11:06 1:11:15 1:11:24 1:11:33 1:11:42 1:11:51 1:12:05 1:12:14 1:12:23 1:12:32 1:12:41 1:12:50 1:13:04 1:13:13 1:13:22 1:13:31 1:13:40 1:14:03 1:14:12 1:14:21 1:14:30 1:15:02 1:15:11 1:15:20 1:16:01 1:16:10 1:17:00 1:20:06 1:20:15 1:20:24 1:20:33 1:20:42 1:20:51 1:21:05 1:21:14 1:21:23 1:21:32 1:21:41 1:21:50 1:22:04 1:22:13 1:22:22 1:22:31 1:22:40 1:23:03 1:23:12 1:23:21 1:23:30 1:24:02 1:24:11 1:24:20 1:25:01 1:25:10 1:26:00 1:30:05 1:30:14 1:30:23 1:30:32 1:30:41 1:30:50 1:31:04 1:31:13 1:31:22 1:31:31 1:31:40 1:32:03 1:32:12 1:32:21 1:32:30 1:33:02 1:33:11 1:33:20 1:34:01 1:34:10 1:35:00 1:40:04 1:40:13 1:40:22 1:40:31 1:40:40 1:41:03 1:41:12 1:41:21 1:41:30 1:42:02 1:42:11 1:42:20 1:43:01 1:43:10 1:44:00 1:50:03 1:50:12 1:50:21 1:50:30 1:51:02 1:51:11 1:51:20 1:52:01 1:52:10 1:53:00 2:00:07 2:00:16 2:00:25 2:00:34 2:00:43 2:00:52 2:01:06 2:01:15 2:01:24 2:01:33 2:01:42 2:01:51 2:02:05 2:02:14 2:02:23 2:02:32 2:02:41 2:02:50 2:03:04 2:03:13 2:03:22 2:03:31 2:03:40 2:04:03 2:04:12 2:04:21 2:04:30 2:05:02 2:05:11 2:05:20 2:06:01 2:06:10 2:07:00 2:10:06 2:10:15 2:10:24 2:10:33 2:10:42 2:10:51 2:11:05 2:11:14 2:11:23 2:11:32 2:11:41 2:11:50 2:12:04 2:12:13 2:12:22 2:12:31 2:12:40 2:13:03 2:13:12 2:13:21 2:13:30 2:14:02 2:14:11 2:14:20 2:15:01 2:15:10 2:16:00 2:20:05 2:20:14 2:20:23 2:20:32 2:20:41 2:20:50 2:21:04 2:21:13 2:21:22 2:21:31 2:21:40 2:22:03 2:22:12 2:22:21 2:22:30 2:23:02 2:23:11 2:23:20 2:24:01 2:24:10 2:25:00 2:30:04 2:30:13 2:30:22 2:30:31 2:30:40 2:31:03 2:31:12 2:31:21 2:31:30 2:32:02 2:32:11 2:32:20 2:33:01 2:33:10 2:34:00 2:40:03 2:40:12 2:40:21 2:40:30 2:41:02 2:41:11 2:41:20 2:42:01 2:42:10 2:43:00 2:50:02 2:50:11 2:50:20 2:51:01 2:51:10 2:52:00 3:00:06 3:00:15 3:00:24 3:00:33 3:00:42 3:00:51 3:01:05 3:01:14 3:01:23 3:01:32 3:01:41 3:01:50 3:02:04 3:02:13 3:02:22 3:02:31 3:02:40 3:03:03 3:03:12 3:03:21 3:03:30 3:04:02 3:04:11 3:04:20 3:05:01 3:05:10 3:06:00 3:10:05 3:10:14 3:10:23 3:10:32 3:10:41 3:10:50 3:11:04 3:11:13 3:11:22 3:11:31 3:11:40 3:12:03 3:12:12 3:12:21 3:12:30 3:13:02 3:13:11 3:13:20 3:14:01 3:14:10 3:15:00 3:20:04 3:20:13 3:20:22 3:20:31 3:20:40 3:21:03 3:21:12 3:21:21 3:21:30 3:22:02 3:22:11 3:22:20 3:23:01 3:23:10 3:24:00 3:30:03 3:30:12 3:30:21 3:30:30 3:31:02 3:31:11 3:31:20 3:32:01 3:32:10 3:33:00 3:40:02 3:40:11 3:40:20 3:41:01 3:41:10 3:42:00 3:50:01 3:50:10 3:51:00 4:00:05 4:00:14 4:00:23 4:00:32 4:00:41 4:00:50 4:01:04 4:01:13 4:01:22 4:01:31 4:01:40 4:02:03 4:02:12 4:02:21 4:02:30 4:03:02 4:03:11 4:03:20 4:04:01 4:04:10 4:05:00 4:10:04 4:10:13 4:10:22 4:10:31 4:10:40 4:11:03 4:11:12 4:11:21 4:11:30 4:12:02 4:12:11 4:12:20 4:13:01 4:13:10 4:14:00 4:20:03 4:20:12 4:20:21 4:20:30 4:21:02 4:21:11 4:21:20 4:22:01 4:22:10 4:23:00 4:30:02 4:30:11 4:30:20 4:31:01 4:31:10 4:32:00 4:40:01 4:40:10 4:41:00 4:50:00 5:00:04 5:00:13 5:00:22 5:00:31 5:00:40 5:01:03 5:01:12 5:01:21 5:01:30 5:02:02 5:02:11 5:02:20 5:03:01 5:03:10 5:04:00 5:10:03 5:10:12 5:10:21 5:10:30 5:11:02 5:11:11 5:11:20 5:12:01 5:12:10 5:13:00 5:20:02 5:20:11 5:20:20 5:21:01 5:21:10 5:22:00 5:30:01 5:30:10 5:31:00 5:40:00 6:00:03 6:00:12 6:00:21 6:00:30 6:01:02 6:01:11 6:01:20 6:02:01 6:02:10 6:03:00 6:10:02 6:10:11 6:10:20 6:11:01 6:11:10 6:12:00 6:20:01 6:20:10 6:21:00 6:30:00 7:00:02 7:00:11 7:00:20 7:01:01 7:01:10 7:02:00 7:10:01 7:10:10 7:11:00 7:20:00 8:00:01 8:00:10 8:01:00 8:10:00 9:00:00 10:00:08 10:00:17 10:00:26 10:00:35 10:00:44 10:00:53 10:01:07 10:01:16 10:01:25 10:01:34 10:01:43 10:01:52 10:02:06 10:02:15 10:02:24 10:02:33 10:02:42 10:02:51 10:03:05 10:03:14 10:03:23 10:03:32 10:03:41 10:03:50 10:04:04 10:04:13 10:04:22 10:04:31 10:04:40 10:05:03 10:05:12 10:05:21 10:05:30 10:06:02 10:06:11 10:06:20 10:07:01 10:07:10 10:08:00 10:10:07 10:10:16 10:10:25 10:10:34 10:10:43 10:10:52 10:11:06 10:11:15 10:11:24 10:11:33 10:11:42 10:11:51 10:12:05 10:12:14 10:12:23 10:12:32 10:12:41 10:12:50 10:13:04 10:13:13 10:13:22 10:13:31 10:13:40 10:14:03 10:14:12 10:14:21 10:14:30 10:15:02 10:15:11 10:15:20 10:16:01 10:16:10 10:17:00 10:20:06 10:20:15 10:20:24 10:20:33 10:20:42 10:20:51 10:21:05 10:21:14 10:21:23 10:21:32 10:21:41 10:21:50 10:22:04 10:22:13 10:22:22 10:22:31 10:22:40 10:23:03 10:23:12 10:23:21 10:23:30 10:24:02 10:24:11 10:24:20 10:25:01 10:25:10 10:26:00 10:30:05 10:30:14 10:30:23 10:30:32 10:30:41 10:30:50 10:31:04 10:31:13 10:31:22 10:31:31 10:31:40 10:32:03 10:32:12 10:32:21 10:32:30 10:33:02 10:33:11 10:33:20 10:34:01 10:34:10 10:35:00 10:40:04 10:40:13 10:40:22 10:40:31 10:40:40 10:41:03 10:41:12 10:41:21 10:41:30 10:42:02 10:42:11 10:42:20 10:43:01 10:43:10 10:44:00 10:50:03 10:50:12 10:50:21 10:50:30 10:51:02 10:51:11 10:51:20 10:52:01 10:52:10 10:53:00 11:00:07 11:00:16 11:00:25 11:00:34 11:00:43 11:00:52 11:01:06 11:01:15 11:01:24 11:01:33 11:01:42 11:01:51 11:02:05 11:02:14 11:02:23 11:02:32 11:02:41 11:02:50 11:03:04 11:03:13 11:03:22 11:03:31 11:03:40 11:04:03 11:04:12 11:04:21 11:04:30 11:05:02 11:05:11 11:05:20 11:06:01 11:06:10 11:07:00 11:10:06 11:10:15 11:10:24 11:10:33 11:10:42 11:10:51 11:11:05 11:11:14 11:11:23 11:11:32 11:11:41 11:11:50 11:12:04 11:12:13 11:12:22 11:12:31 11:12:40 11:13:03 11:13:12 11:13:21 11:13:30 11:14:02 11:14:11 11:14:20 11:15:01 11:15:10 11:16:00 11:20:05 11:20:14 11:20:23 11:20:32 11:20:41 11:20:50 11:21:04 11:21:13 11:21:22 11:21:31 11:21:40 11:22:03 11:22:12 11:22:21 11:22:30 11:23:02 11:23:11 11:23:20 11:24:01 11:24:10 11:25:00 11:30:04 11:30:13 11:30:22 11:30:31 11:30:40 11:31:03 11:31:12 11:31:21 11:31:30 11:32:02 11:32:11 11:32:20 11:33:01 11:33:10 11:34:00 11:40:03 11:40:12 11:40:21 11:40:30 11:41:02 11:41:11 11:41:20 11:42:01 11:42:10 11:43:00 11:50:02 11:50:11 11:50:20 11:51:01 11:51:10 11:52:00 12:00:06 12:00:15 12:00:24 12:00:33 12:00:42 12:00:51 12:01:05 12:01:14 12:01:23 12:01:32 12:01:41 12:01:50 12:02:04 12:02:13 12:02:22 12:02:31 12:02:40 12:03:03 12:03:12 12:03:21 12:03:30 12:04:02 12:04:11 12:04:20 12:05:01 12:05:10 12:06:00 12:10:05 12:10:14 12:10:23 12:10:32 12:10:41 12:10:50 12:11:04 12:11:13 12:11:22 12:11:31 12:11:40 12:12:03 12:12:12 12:12:21 12:12:30 12:13:02 12:13:11 12:13:20 12:14:01 12:14:10 12:15:00 12:20:04 12:20:13 12:20:22 12:20:31 12:20:40 12:21:03 12:21:12 12:21:21 12:21:30 12:22:02 12:22:11 12:22:20 12:23:01 12:23:10 12:24:00 12:30:03 12:30:12 12:30:21 12:30:30 12:31:02 12:31:11 12:31:20 12:32:01 12:32:10 12:33:00 12:40:02 12:40:11 12:40:20 12:41:01 12:41:10 12:42:00 12:50:01 12:50:10 12:51:00

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Over a day, a 24 hour digital clock without seconds will display 107 such times:

0:09 0:18 0:27 0:36 0:45 0:54 1:08 1:17 1:26 1:35 1:44 1:53 2:07 2:16 2:25 2:34 2:43 2:52 3:06 3:15 3:24 3:33 3:42 3:51 4:05 4:14 4:23 4:32 4:41 4:50 5:04 5:13 5:22 5:31 5:40 6:03 6:12 6:21 6:30 7:02 7:11 7:20 8:01 8:10 9:00 10:08 10:17 10:26 10:35 10:44 10:53 11:07 11:16 11:25 11:34 11:43 11:52 12:06 12:15 12:24 12:33 12:42 12:51 13:05 13:14 13:23 13:32 13:41 13:50 14:04 14:13 14:22 14:31 14:40 15:03 15:12 15:21 15:30 16:02 16:11 16:20 17:01 17:10 18:00 20:07 20:16 20:25 20:34 20:43 20:52 21:06 21:15 21:24 21:33 21:42 21:51 22:05 22:14 22:23 22:32 22:41 22:50 23:04 23:13 23:22 23:31 23:40

With seconds it displays 1395 such times:

0:00:09 0:00:18 0:00:27 0:00:36 0:00:45 0:00:54 0:01:08 0:01:17 0:01:26 0:01:35 0:01:44 0:01:53 0:02:07 0:02:16 0:02:25 0:02:34 0:02:43 0:02:52 0:03:06 0:03:15 0:03:24 0:03:33

...

23:03:10 23:04:00 23:10:03 23:10:12 23:10:21 23:10:30 23:11:02 23:11:11 23:11:20 23:12:01 23:12:10 23:13:00 23:20:02 23:20:11 23:20:20 23:21:01 23:21:10 23:22:00 23:30:01 23:30:10 23:31:00 23:40:00

Answer 3

2