Question

How many times in a 12 hour period does the sum of the digits on a digital clock equal 6? (For example. 1:32 = 1+3+2 = 6

Answer 1

We only consider the time periods between 1:00 and 6:00, since before and after this interval, the sum will always be larger than 6.

From 1:00 - 1:59
Sum of the minute digits must be 5
05, 50, 14, 41, 23, 32

From 2:00 - 2:59
Sum of the minute digits must be 4
04, 40, 22, 13, 31

From 3:00 - 3:59
Sum of the minute digits must be 3
12, 21, 30, 03

From 4:00 - 4:59
Sum of the minute digits must be 2
11, 02, 20

From 5:00 - 5:59
Sum of the minute digits must be 1
01, 10

And of course, 6:00

That totals to 21 times.

Answer 2

what about 11:04 11:13 12:03 and 12:30 and so on?

Answer 3

Whoops, forgot 10:00 - 12:59, my bad

However, you could use the same method to identify those too.