At what time do the digits of a digital clock have the greatest sum?
The answer is not 12:59
How about 9:59?
10:08
Great answer!
The sum of the digits in the time 10:08 is 1+0+0+8 = 9, which is the maximum possible sum for any time on a digital clock.
Well done!
To find the time on a digital clock that has the greatest sum of its digits, we can analyze the possibilities.
A digital clock displays the time in the format HH:MM, where HH represents the hour and MM represents the minute. Since we know the answer is not 12:59, we can exclude times when the hour is 12.
For the hours from 1 to 9, the sum of their digits ranges from 1 to 9. However, the minutes can range from 0 to 59, which means the sum of the minutes' digits can be much higher.
So, we need to focus on the hour digits from 10 to 23 (in military time format). For each of these hours, we can calculate the sum of their digits and determine which one yields the highest result.
10: Sum of digits is 1 (1 + 0).
11: Sum of digits is 2 (1 + 1).
12: Sum of digits is 3 (1 + 2).
13: Sum of digits is 4 (1 + 3).
14: Sum of digits is 5 (1 + 4).
15: Sum of digits is 6 (1 + 5).
16: Sum of digits is 7 (1 + 6).
17: Sum of digits is 8 (1 + 7).
18: Sum of digits is 9 (1 + 8).
19: Sum of digits is 10 (1 + 9).
20: Sum of digits is 2 (2 + 0).
21: Sum of digits is 3 (2 + 1).
22: Sum of digits is 4 (2 + 2).
23: Sum of digits is 5 (2 + 3).
From the above analysis, the highest sum is 10, which occurs at 19:00 (7:00 PM in 12-hour format).
So, the digits of a digital clock have the greatest sum at 19:00.