Sitting on a bus one day in Iran, as we were driving through the desert, I was looking at a digital 7-segment clock at the front of the bus. Near the clock was a convex mirror, used by the driver to allow him to see everyone in the back. In noticed the reflection of the clock in the mirror, and it amused me that sometimes the value displayed on the mirror image of the clock would still be a valid time.

This got me thinking about how many times are valid when reversed horizontally in a mirror (e.g. 00:51 = 12:00). I also wondered how many times are valid when reversed vertically in a mirror (e.g. 11:06 = 11:09), when rotated by 180 degrees (e.g. 10:20 = 05:01) and when the number order is reversed (e.g. 00:32 = 23:00). And, of course, for each of these how many are valid given a 12 hour clock (12:00 to 11:59) as well as a 24 hour clock (00:00 to 23:59).

The tables below are the fruits of my labour. I'm sure there must be a better way of describing this, with animation and maybe a 7 segment display font!

24 Hour Clock

Time Vertical Horizontal Rotated Reversed
00:00 00:00 00:00 00:00 00:00
00:01 00:01 10:00 10:00 10:00
00:02 00:05 20:00
00:03 00:03
00:05 00:02 20:00 20:00
00:08 00:08
00:10 00:10 01:00 01:00 01:00
00:11 00:11 11:00 11:00 11:00
00:12 00:15 21:00
00:15 00:12 21:00 21:00
00:18 00:18
00:20 00:50 05:00 05:00 02:00
00:21 00:51 15:00 15:00 12:00
00:22 00:55 22:00
00:23 00:53
00:25 00:52
00:28 00:58
00:30 00:30 03:00
00:31 00:31 13:00
00:32 00:35 23:00
00:33 00:33
00:35 00:32
00:38 00:38
00:40 04:00
00:41 14:00
00:50 00:20 02:00 02:00 05:00
00:51 00:21 12:00 12:00 15:00
00:52 00:25
00:53 00:23
00:55 00:22 22:00 22:00
00:58 00:28
01:00 01:00 00:10 00:10 00:10
01:01 01:01 10:10 10:10 10:10
01:02 01:05 20:10
01:03 01:03
01:05 01:02 20:10 20:10
01:08 01:08
01:10 01:10 01:10 01:10 01:10
01:11 01:11 11:10 11:10 11:10
01:12 01:15 21:10
01:15 01:12 21:10 21:10
01:18 01:18
01:20 01:50 05:10 05:10 02:10
01:21 01:51 15:10 15:10 12:10
01:22 01:55 22:10
01:23 01:53
01:25 01:52
01:28 01:58
01:30 01:30 03:10
01:31 01:31 13:10
01:32 01:35 23:10
01:33 01:33
01:35 01:32
01:38 01:38
01:40 04:10
01:41 14:10
01:50 01:20 02:10 02:10 05:10
01:51 01:21 12:10 12:10 15:10
01:52 01:25
01:53 01:23
01:55 01:22 22:10 22:10
01:58 01:28
02:00 05:00 00:50 00:50 00:20
02:01 05:01 10:50 10:50 10:20
02:02 05:05 20:20
02:03 05:03
02:05 05:02 20:50 20:50
02:08 05:08
02:10 05:10 01:50 01:50 01:20
02:11 05:11 11:50 11:50 11:20
02:12 05:15 21:20
02:15 05:12 21:50 21:50
02:18 05:18
02:20 05:50 05:50 05:50 02:20
02:21 05:51 15:50 15:50 12:20
02:22 05:55 22:20
02:23 05:53
02:25 05:52
02:28 05:58
02:30 05:30 03:20
02:31 05:31 13:20
02:32 05:35 23:20
02:33 05:33
02:35 05:32
02:38 05:38
02:40 04:20
02:41 14:20
02:50 05:20 02:50 02:50 05:20
02:51 05:21 12:50 12:50 15:20
02:52 05:25
02:53 05:23
02:55 05:22 22:50 22:50
02:58 05:28
03:00 03:00 00:30
03:01 03:01 10:30
03:02 03:05 20:30
03:03 03:03
03:05 03:02
03:08 03:08
03:10 03:10 01:30
03:11 03:11 11:30
03:12 03:15 21:30
03:15 03:12
03:18 03:18
03:20 03:50 02:30
03:21 03:51 12:30
03:22 03:55 22:30
03:23 03:53
03:25 03:52
03:28 03:58
03:30 03:30 03:30
03:31 03:31 13:30
03:32 03:35 23:30
03:33 03:33
03:35 03:32
03:38 03:38
03:40 04:30
03:41 14:30
03:50 03:20 05:30
03:51 03:21 15:30
03:52 03:25
03:53 03:23
03:55 03:22
03:58 03:28
04:00 00:40
04:01 10:40
04:02 20:40
04:10 01:40
04:11 11:40
04:12 21:40
04:20 02:40
04:21 12:40
04:22 22:40
04:30 03:40
04:31 13:40
04:32 23:40
04:40 04:40
04:41 14:40
04:50 05:40
04:51 15:40
05:00 02:00 00:20 00:20 00:50
05:01 02:01 10:20 10:20 10:50
05:02 02:05 20:50
05:03 02:03
05:05 02:02 20:20 20:20
05:08 02:08
05:10 02:10 01:20 01:20 01:50
05:11 02:11 11:20 11:20 11:50
05:12 02:15 21:50
05:15 02:12 21:20 21:20
05:18 02:18
05:20 02:50 05:20 05:20 02:50
05:21 02:51 15:20 15:20 12:50
05:22 02:55 22:50
05:23 02:53
05:25 02:52
05:28 02:58
05:30 02:30 03:50
05:31 02:31 13:50
05:32 02:35 23:50
05:33 02:33
05:35 02:32
05:38 02:38
05:40 04:50
05:41 14:50
05:50 02:20 02:20 02:20 05:50
05:51 02:21 12:20 12:20 15:50
05:52 02:25
05:53 02:23
05:55 02:22 22:20 22:20
05:58 02:28
08:00 08:00
08:01 08:01
08:02 08:05
08:03 08:03
08:05 08:02
08:08 08:08
08:10 08:10
08:11 08:11
08:12 08:15
08:15 08:12
08:18 08:18
08:20 08:50
08:21 08:51
08:22 08:55
08:23 08:53
08:25 08:52
08:28 08:58
08:30 08:30
08:31 08:31
08:32 08:35
08:33 08:33
08:35 08:32
08:38 08:38
08:50 08:20
08:51 08:21
08:52 08:25
08:53 08:23
08:55 08:22
08:58 08:28
10:00 10:00 00:01 00:01 00:01
10:01 10:01 10:01 10:01 10:01
10:02 10:05 20:01
10:03 10:03
10:05 10:02 20:01 20:01
10:08 10:08
10:10 10:10 01:01 01:01 01:01
10:11 10:11 11:01 11:01 11:01
10:12 10:15 21:01
10:15 10:12 21:01 21:01
10:18 10:18
10:20 10:50 05:01 05:01 02:01
10:21 10:51 15:01 15:01 12:01
10:22 10:55 22:01
10:23 10:53
10:25 10:52
10:28 10:58
10:30 10:30 03:01
10:31 10:31 13:01
10:32 10:35 23:01
10:33 10:33
10:35 10:32
10:38 10:38
10:40 04:01
10:41 14:01
10:50 10:20 02:01 02:01 05:01
10:51 10:21 12:01 12:01 15:01
10:52 10:25
10:53 10:23
10:55 10:22 22:01 22:01
10:58 10:28
11:00 11:00 00:11 00:11 00:11
11:01 11:01 10:11 10:11 10:11
11:02 11:05 20:11
11:03 11:03
11:05 11:02 20:11 20:11
11:08 11:08
11:10 11:10 01:11 01:11 01:11
11:11 11:11 11:11 11:11 11:11
11:12 11:15 21:11
11:15 11:12 21:11 21:11
11:18 11:18
11:20 11:50 05:11 05:11 02:11
11:21 11:51 15:11 15:11 12:11
11:22 11:55 22:11
11:23 11:53
11:25 11:52
11:28 11:58
11:30 11:30 03:11
11:31 11:31 13:11
11:32 11:35 23:11
11:33 11:33
11:35 11:32
11:38 11:38
11:40 04:11
11:41 14:11
11:50 11:20 02:11 02:11 05:11
11:51 11:21 12:11 12:11 15:11
11:52 11:25
11:53 11:23
11:55 11:22 22:11 22:11
11:58 11:28
12:00 15:00 00:51 00:21
12:01 15:01 10:51 10:21
12:02 15:05 20:21
12:03 15:03
12:05 15:02 20:51
12:08 15:08
12:10 15:10 01:51 01:21
12:11 15:11 11:51 11:21
12:12 15:15 21:21
12:15 15:12 21:51
12:18 15:18
12:20 15:50 05:51 02:21
12:21 15:51 15:51 12:21
12:22 15:55 22:21
12:23 15:53
12:25 15:52
12:28 15:58
12:30 15:30 03:21
12:31 15:31 13:21
12:32 15:35 23:21
12:33 15:33
12:35 15:32
12:38 15:38
12:40 04:21
12:41 14:21
12:50 15:20 02:51 05:21
12:51 15:21 12:51 15:21
12:52 15:25
12:53 15:23
12:55 15:22 22:51
12:58 15:28
13:00 00:31
13:01 10:31
13:02 20:31
13:10 01:31
13:11 11:31
13:12 21:31
13:20 02:31
13:21 12:31
13:22 22:31
13:30 03:31
13:31 13:31
13:32 23:31
13:40 04:31
13:41 14:31
13:50 05:31
13:51 15:31
14:00 00:41
14:01 10:41
14:02 20:41
14:10 01:41
14:11 11:41
14:12 21:41
14:20 02:41
14:21 12:41
14:22 22:41
14:30 03:41
14:31 13:41
14:32 23:41
14:40 04:41
14:41 14:41
14:50 05:41
14:51 15:41
15:00 12:00 00:21 00:21 00:51
15:01 12:01 10:21 10:21 10:51
15:02 12:05 20:51
15:03 12:03
15:05 12:02 20:21 20:21
15:08 12:08
15:10 12:10 01:21 01:21 01:51
15:11 12:11 11:21 11:21 11:51
15:12 12:15 21:51
15:15 12:12 21:21 21:21
15:18 12:18
15:20 12:50 05:21 05:21 02:51
15:21 12:51 15:21 15:21 12:51
15:22 12:55 22:51
15:23 12:53
15:25 12:52
15:28 12:58
15:30 12:30 03:51
15:31 12:31 13:51
15:32 12:35 23:51
15:33 12:33
15:35 12:32
15:38 12:38
15:40 04:51
15:41 14:51
15:50 12:20 02:21 02:21 05:51
15:51 12:21 12:21 12:21 15:51
15:52 12:25
15:53 12:23
15:55 12:22 22:21 22:21
15:58 12:28
18:00 18:00
18:01 18:01
18:02 18:05
18:03 18:03
18:05 18:02
18:08 18:08
18:10 18:10
18:11 18:11
18:12 18:15
18:15 18:12
18:18 18:18
18:20 18:50
18:21 18:51
18:22 18:55
18:23 18:53
18:25 18:52
18:28 18:58
18:30 18:30
18:31 18:31
18:32 18:35
18:33 18:33
18:35 18:32
18:38 18:38
18:50 18:20
18:51 18:21
18:52 18:25
18:53 18:23
18:55 18:22
18:58 18:28
20:00 00:05 00:05 00:02
20:01 10:05 10:05 10:02
20:02 20:02
20:05 20:05 20:05
20:10 01:05 01:05 01:02
20:11 11:05 11:05 11:02
20:12 21:02
20:15 21:05 21:05
20:20 05:05 05:05 02:02
20:21 15:05 15:05 12:02
20:22 22:02
20:30 03:02
20:31 13:02
20:32 23:02
20:40 04:02
20:41 14:02
20:50 02:05 02:05 05:02
20:51 12:05 12:05 15:02
20:55 22:05 22:05
21:00 00:15 00:15 00:12
21:01 10:15 10:15 10:12
21:02 20:12
21:05 20:15 20:15
21:10 01:15 01:15 01:12
21:11 11:15 11:15 11:12
21:12 21:12
21:15 21:15 21:15
21:20 05:15 05:15 02:12
21:21 15:15 15:15 12:12
21:22 22:12
21:30 03:12
21:31 13:12
21:32 23:12
21:40 04:12
21:41 14:12
21:50 02:15 02:15 05:12
21:51 12:15 12:15 15:12
21:55 22:15 22:15
22:00 00:55 00:22
22:01 10:55 10:22
22:02 20:22
22:05 20:55
22:10 01:55 01:22
22:11 11:55 11:22
22:12 21:22
22:15 21:55
22:20 05:55 02:22
22:21 15:55 12:22
22:22 22:22
22:30 03:22
22:31 13:22
22:32 23:22
22:40 04:22
22:41 14:22
22:50 02:55 05:22
22:51 12:55 15:22
22:55 22:55
23:00 00:32
23:01 10:32
23:02 20:32
23:10 01:32
23:11 11:32
23:12 21:32
23:20 02:32
23:21 12:32
23:22 22:32
23:30 03:32
23:31 13:32
23:32 23:32
23:40 04:32
23:41 14:32
23:50 05:32
23:51 15:32

12 Hour Clock

Time Vertical Horizontal Rotated Reversed
01:00 01:00
01:01 01:01 10:10 10:10 10:10
01:02 01:05
01:03 01:03
01:05 01:02
01:08 01:08
01:10 01:10 01:10 01:10 01:10
01:11 01:11 11:10 11:10 11:10
01:12 01:15
01:15 01:12
01:18 01:18
01:20 01:50 05:10 05:10 02:10
01:21 01:51 12:10
01:22 01:55
01:23 01:53
01:25 01:52
01:28 01:58
01:30 01:30 03:10
01:31 01:31
01:32 01:35
01:33 01:33
01:35 01:32
01:38 01:38
01:40 04:10
01:50 01:20 02:10 02:10 05:10
01:51 01:21 12:10 12:10
01:52 01:25
01:53 01:23
01:55 01:22
01:58 01:28
02:00 05:00
02:01 05:01 10:50 10:50 10:20
02:02 05:05
02:03 05:03
02:05 05:02
02:08 05:08
02:10 05:10 01:50 01:50 01:20
02:11 05:11 11:50 11:50 11:20
02:12 05:15
02:15 05:12
02:18 05:18
02:20 05:50 05:50 05:50 02:20
02:21 05:51 12:20
02:22 05:55
02:23 05:53
02:25 05:52
02:28 05:58
02:30 05:30 03:20
02:31 05:31
02:32 05:35
02:33 05:33
02:35 05:32
02:38 05:38
02:40 04:20
02:50 05:20 02:50 02:50 05:20
02:51 05:21 12:50 12:50
02:52 05:25
02:53 05:23
02:55 05:22
02:58 05:28
03:00 03:00
03:01 03:01 10:30
03:02 03:05
03:03 03:03
03:05 03:02
03:08 03:08
03:10 03:10 01:30
03:11 03:11 11:30
03:12 03:15
03:15 03:12
03:18 03:18
03:20 03:50 02:30
03:21 03:51 12:30
03:22 03:55
03:23 03:53
03:25 03:52
03:28 03:58
03:30 03:30 03:30
03:31 03:31
03:32 03:35
03:33 03:33
03:35 03:32
03:38 03:38
03:40 04:30
03:50 03:20 05:30
03:51 03:21
03:52 03:25
03:53 03:23
03:55 03:22
03:58 03:28
04:01 10:40
04:10 01:40
04:11 11:40
04:20 02:40
04:21 12:40
04:30 03:40
04:40 04:40
04:50 05:40
05:00 02:00
05:01 02:01 10:20 10:20 10:50
05:02 02:05
05:03 02:03
05:05 02:02
05:08 02:08
05:10 02:10 01:20 01:20 01:50
05:11 02:11 11:20 11:20 11:50
05:12 02:15
05:15 02:12
05:18 02:18
05:20 02:50 05:20 05:20 02:50
05:21 02:51 12:50
05:22 02:55
05:23 02:53
05:25 02:52
05:28 02:58
05:30 02:30 03:50
05:31 02:31
05:32 02:35
05:33 02:33
05:35 02:32
05:38 02:38
05:40 04:50
05:50 02:20 02:20 02:20 05:50
05:51 02:21 12:20 12:20
05:52 02:25
05:53 02:23
05:55 02:22
05:58 02:28
08:00 08:00
08:01 08:01
08:02 08:05
08:03 08:03
08:05 08:02
08:08 08:08
08:10 08:10
08:11 08:11
08:12 08:15
08:15 08:12
08:18 08:18
08:20 08:50
08:21 08:51
08:22 08:55
08:23 08:53
08:25 08:52
08:28 08:58
08:30 08:30
08:31 08:31
08:32 08:35
08:33 08:33
08:35 08:32
08:38 08:38
08:50 08:20
08:51 08:21
08:52 08:25
08:53 08:23
08:55 08:22
08:58 08:28
10:00 10:00
10:01 10:01 10:01 10:01 10:01
10:02 10:05
10:03 10:03
10:05 10:02
10:08 10:08
10:10 10:10 01:01 01:01 01:01
10:11 10:11 11:01 11:01 11:01
10:12 10:15
10:15 10:12
10:18 10:18
10:20 10:50 05:01 05:01 02:01
10:21 10:51 12:01
10:22 10:55
10:23 10:53
10:25 10:52
10:28 10:58
10:30 10:30 03:01
10:31 10:31
10:32 10:35
10:33 10:33
10:35 10:32
10:38 10:38
10:40 04:01
10:50 10:20 02:01 02:01 05:01
10:51 10:21 12:01 12:01
10:52 10:25
10:53 10:23
10:55 10:22
10:58 10:28
11:00 11:00
11:01 11:01 10:11 10:11 10:11
11:02 11:05
11:03 11:03
11:05 11:02
11:08 11:08
11:10 11:10 01:11 01:11 01:11
11:11 11:11 11:11 11:11 11:11
11:12 11:15
11:15 11:12
11:18 11:18
11:20 11:50 05:11 05:11 02:11
11:21 11:51 12:11
11:22 11:55
11:23 11:53
11:25 11:52
11:28 11:58
11:30 11:30 03:11
11:31 11:31
11:32 11:35
11:33 11:33
11:35 11:32
11:38 11:38
11:40 04:11
11:50 11:20 02:11 02:11 05:11
11:51 11:21 12:11 12:11
11:52 11:25
11:53 11:23
11:55 11:22
11:58 11:28
12:01 10:51 10:21
12:10 01:51 01:21
12:11 11:51 11:21
12:20 05:51 02:21
12:21 12:21
12:30 03:21
12:40 04:21
12:50 02:51 05:21
12:51 12:51

Code