At what time do the digits of a digital clock have the greatest sum?
The answer is not 12:59. it is other than this
To determine at what time the digits of a digital clock have the greatest sum, we can break down the hours and minutes into individual digits.
A digital clock typically displays the time in the format HH:MM, where HH represents the hours and MM represents the minutes.
Let's start with the hours (HH) part. The hours on a digital clock range from 00 to 23 since it follows the 24-hour format.
If we check all the possibilities, we find that the greatest sum for the hour digits occurs at 19:59. The sum of the digits in 19 is 1+9 = 10, and the sum of the digits in 59 is 5+9 = 14. Therefore, at 19:59, the digit sum is 10 + 14 = 24.
Next, let's move on to the minutes (MM) part. The minutes on a digital clock range from 00 to 59.
Again, checking all the possibilities, we find that the greatest sum for the minute digits occurs at 09:59. The sum of the digits in 09 is 0+9 = 9, and the sum of the digits in 59 is 5+9 = 14. Therefore, at 09:59, the digit sum is 9 + 14 = 23.
Comparing the two, we see that the digit sum for the hours is greater at 19:59 (24) compared to the digit sum for the minutes at 09:59 (23).
Hence, the time at which the digits of a digital clock have the greatest sum other than 12:59 is 19:59.