What is the least possible sum of digits displaying time on a 12 hour clock?

We can't get a zero (e.g. no 0:00), but we can get a 1 (e.g. 1:00 or 10:00).

1 + 0 + 0 = 1

1 + 0 + 0 + 0 = 1

(The maximum possible would be at time 9:59 --> 9 + 5 + 9 = 23)

Answer:

The smallest possible sum of the digits is 1.

3

if you only have the '12' to indicate noon and midnight,

12

then there are clocks with 3,6,9, and 12

30

if the problem is to add 1 through 12

12(12+1)/2

6(13)

78

Smallest possible sum is 1, which occurs at 1:00 or 10:00