In exactly 12 hours, for how many minutes is the sum of the digits on an electronic digital clock greater than 15? (Use just the digits that give the hour and the minute.)
Let’s start at noon and count until midnight.
For 12:00 hour: 12:58, 12:59 – that’s 2 times.
For 1:00 hour: none work.
For 2:00 hour: 2:59 – that’s 1 more.
For 3:00 hour: 3:49, 3:58, 3:59 – that’s 3 more.
For 4:00 hour: 4:39, 4:48, 4:49, 4:57, 4:58, 4:59 – that’s 6 more.
For 5:00 hour: 5:29, 5:38, 5:39, 5:47, 5:48, 5:49, 5:56, 5:57, 5:58, 5:59 – that’s 10 more.
For 6:00 hour: 15 more.
For 7:00 hour: 21 more.
For 8:00 hour: 28 more.
For 9:00 hour: 36 more.
For 10:00 hour: none work (like 1:00 hour).
For 11:00 hour: 11:59 (like 2:00 hour).
We have a grand total of 123 times in a 12-hour period that the sum of the digits on a digital clock exceeds 15.