Time Puzzle

[Joseph Bolas]

The following picture below shows the time 07:19 as displayed on some 24-hour LCD clocks:



Now if you add the numbers together you get 17 (0+7+1+9) and if you add the segments together you get 17 again (6+3+2+6) (also 09:17, 17:09 and 19:07 total 17 as well).

There is a total of 50 times from 00:00 - 23:59 (including the 4 mentioned above) where the numbers on the display total the number of segments used. For the purpose of this puzzle, this is how the numbers would look:



How any of the remaining 46 times can you find? So this puzzle lasts a few days, please only post a maximum of 5 times that you have found

[Dinos Sfyris]

Found them all in under an hour using a systematic method which I can't be bothered to explain as I'm going to watch some live Countdown tomorrow so need to be up early. Will do the first 5 chronologically! That will save the others some time!

The following "sum of digits = number of segments" times take place between midnight and 11am. Events occur in real time

07:19 (0+7+1+9)=(6+3+2+6)=17
07:37 (0+7+3+7)=(6+3+5+3)=17
09:17 (0+9+1+7)=(6+6+2+3)=17
09:49 (0+9+4+9)=(6+6+4+6)=22
09:59 (0+9+5+9)=(6+6+5+6)=23

The first and 3rd happen to be in Josephs example but I thought I'd keep it chronological.

Starter's tip: Notice 4, 5 and 6 are made of 4, 5 and 6 segments respectively so are interchangeable (except you cant put a 6 in the 10s of minutes position)

[Joseph Bolas]

They are the first 5 Dinos . It's now roughly been a week since I started this puzzle off and I don't think anyone else is going to find any other times, so you might as well post the answers Dinos and your method (if you want)

[Dinos Sfyris]

Meh cant be bothered typing out the other 45 times tbh but basically my method was first to write down each digit 1-9 and the number of segments that make it and the difference between the two eg

Digits Segments Difference
0 6 +6
1 2 +1
2 5 +3
3 5 +2
4 4 0
5 5 0
6 6 0
7 3 -4
8 7 -1
9 6 -3

For each valid time the total of the 4 digit-segment differences must equal zero, then I went through each hour to find possible minute digit combinations.

eg for 00:XX the segments - digits difference for the first 2 numbers = 6 + 6 - 0 - 0 = 12 so the remaining digits must have a total difference of -12 for which there are no possibilities. Also obviously each combination must be valid on the 24hr clock eg you can't have 01:79.

[Joseph Bolas]

There are the 50 times that you should have Dinos

07:19, 07:37, 09:17, 09:49, 09:59, 11:19, 11:37, 12:47, 12:57, 13:17,
13:49, 13:59, 14:27, 14:39, 14:48, 14:58, 15:27, 15:39, 15:48, 15:58,
16:27, 16:39, 16:48, 16:58, 17:09, 17:13, 17:24, 17:25, 17:26, 17:31,
17:42, 17:52, 18:18, 18:29, 18:44, 18:45, 18:46, 18:54, 18:55, 18:56,
19:07, 19:11, 19:28, 19:34, 19:35, 19:36, 19:43, 19:53, 21:47, 21:57.