I have a digital clock that shows the time (hours and minutes, in standard AM/PM format) as four digits. Each digit is formed by lighted segments: digits from 0 to 9 have 6, 2, 5, 5, 4, 5, 6, 3, 7, and 6 segments respectively. If the leftmost digit should be a "0", a blank is shown instead.

What's the earliest time when the sum of the segments equal the sum of the digits comprising the time? The latest time? The time with more/less lighted segments?

With an assumption that earliest time is defined as the time where the digits representing it are those that would represent a value closest to 0, with priority hour then minutes (and PM > AM), the time when the sum of the segments equal the sum of the comprising digits representing the time would be:

Earliest = 1:27 AM [# segments = 10]

Latest = 12:57 PM [# segments = 15]

Most = 8:38 AM|PM [# segments = 19]*

Fewest = 1:27 AM|PM [# segments = 10]*


*If the number of segments are not required to equal the value of the sum of digits for the most and fewest segments, the following are the answers:           

Most = 10:08 AM|PM [# segments = 21]

Fewest = 1:11 AM|PM [# segments = 6]  

Edited on June 26, 2012, 1:44 am

Posted by Dej Mar on 2012-06-25 23:29:50