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
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.
what about 11:04 11:13 12:03 and 12:30 and so on?
Whoops, forgot 10:00 - 12:59, my bad
However, you could use the same method to identify those too.
To find out how many times in a 12-hour period the sum of the digits on a digital clock equals 6, we can break the problem down into two parts: counting the number of occurrences in the morning (12:00 AM to 11:59 AM) and the number of occurrences in the afternoon (12:00 PM to 11:59 PM).
For the morning period (12:00 AM to 11:59 AM):
1. Start by considering the hour digits. Since the maximum value for the hour digit is 11, we need to check the following possibilities: 0, 1, 2, 3.
- For the hour digit 0, the possible minute values are limited to 0 to 5 inclusive.
- For the hour digits 1, 2, and 3, the possible minute values range from 0 to 9.
2. Calculate the sum of the digits for each possibility and check if it equals 6.
For the afternoon period (12:00 PM to 11:59 PM):
1. Repeat the same process as above, considering the hour digits from 12 to 23 and the corresponding minute values.
By going through all the possibilities and checking the sum of the digits, you should be able to determine the total number of occurrences in a 12-hour period where the sum of the digits on a digital clock equals 6.