In a twelve hour period of time, for how many minutes is the sum of digits on a digital clock greater than 15?

Answer 1

I'm interpreting this problem as asking how often the sum of the individual digits add up to at least 16. For example, between 11:00 and 12:00, the only time that qualifies is 11:59: 1 + 1 + 5 + 9 = 16.

Given that, this is pretty much a counting exercise. For each one hour range, the number of times that qualify are:

1:00 to 1:59 - 0
2:00 to 2:59 - 1
3:00 to 3:59 - 3
4:00 to 4:59 - 6
5:00 to 5:59 - 10
6:00 to 6:59 - 15
7:00 to 7:59 - 21
8:00 to 8:59 - 27
9:00 to 9:59 - 33
10:00 to 10:59 - 0
11:00 to 11:59 - 1
12:00 to 12:59 - 3

Total: 120

Answer 2

If you're talking about a clock that isn't in military time the following would work.

Find the time which produces a value greater than 15, that would be
2:59: 2+5+9 = 16 Because 5 and 9 in the minute portion of the time will provide the largest sum, it means that in the first hour there are no number combinations that would add up to a value greater than 15, and in the second hour there is 1... If you follow this pattern, you can determine the answer.

Answer 3

Ok, in order to do this, I had to use an excel spreadsheet.
whew.

120.

I set up a column for each of the numbers 1-9 and two columns for 10, 11 and 12. (Since each digit must be added separately).

Then it was a simple matter to set up a formula to figure the totals of the digits, and total those whose sums were over 15.

If you want the spreadsheet, I'll email it to you.

Answer 4

This is a lot of work, you can do it, just take 12:00 and start adding the 15's until you get to 12:00 again. 12:16,12,:17,etc. I think it is 540 ?or 9?