# Digital Alarm Clock

Most of the alarm clock's bulbs are busted as shown above in black shades. Although still working it is not possible to tell what time is it. If we can fix it to display a pattern every seconds, maybe it will be possible to tell time.
How can it show the Hours,Minutes and Seconds of the day in 12H format?

• Not sure if I quite understand the question. Are you saying that the only LCD segments which work are the ones forming the two "8"s either side of the right-hand colon, and the colon itself? What about the "SAT" and "PM"? – Rand al'Thor Oct 23 '16 at 18:38
• note.We cant fix the busted bulbs – TSLF Oct 23 '16 at 18:39
• @randal'thor- we can leave them they are working properly – TSLF Oct 23 '16 at 18:41

If I'm understanding the question correctly, the only working segments are those forming the "8"s either side of the right-hand colon, together with this colon itself:

Each one of these segments can be switched on and off if required, but the broken segments can't be fixed. Since there are 16 different working lights and 2 different settings for each, the total number of possibilities we can display using the clock as shown is $2^{16}=65536$.

But the number of possibilities for the time of day in hours, minutes, and seconds, shown using the 12-hour system, is $12*60*60=43200$. This is less than $65536$, so we can display all possible times of day using only the working segments of the clock.

• What time is it in your design? – TSLF Oct 23 '16 at 19:00
• So if I understand correctly, you assume that the AM/PM display still works? -- Ah, indeed, OP says 12h format. Also, you missed some braces in 2^{16}. – Matsmath Oct 23 '16 at 19:45
• This only works if you can control the two parts of the colon individually, right? – 2012rcampion Oct 23 '16 at 22:56
• @TSLF The segments shown would indicate a value outside of the 43200-second range. – LegionMammal978 Oct 24 '16 at 0:52
• If we want to make it readble , we can use the perimeter of 8 that is like 0- bothe side for the minute and seconds while the colon dots and the center element of both 8's for the hour - [ 0] [ -:-] [ 0] for MM:HH:SS , w/ combininations:( 2^6) (2^4) (2^6) =(64)(16)(64) – TSLF Oct 24 '16 at 3:37

The clockwise sequence patterns for 12-Hours and 60-Min/Sec