How many times in a 24-hour period do the display and its reflection give the same time?

Kindly provided by UKMT Beatrix has a 24-hour digital clock on a glass table-top next to her desk. When she looked at the clock at 13:08, she noticed that the reflected display also read 13:08 (as shown above).
How many times in a 24-hour period do the display and its reflection give the same time?
14 Comments
HARE RAM AGARWAL
19/8/2015 03:47:54 am
96 times the display and reflection will be same. (using permutation)
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Anand Mehta
19/8/2015 04:14:49 am
Only 4 digits possible: 0,1,3 and 8.
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Timothy Tran
20/8/2015 04:54:49 am
Same method.
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24/8/2015 11:28:05 am
Timothy...I tried this where "2" reflects as a "5" and visa versa, but the reflection changes the time indicated. 12:50 is not the same time as its reflection 15:20. 19/8/2015 02:01:04 pm
This is a combinatorics problem. The valid choices for each digit are:
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Paul
19/8/2015 11:30:05 pm
Thanks to Hare Ram, Anand and Pierre for your solutions. As ever, I'm always interested to know how you achieved you solutions, and if there are any alternative methods etc.
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Hare Ram Agarwal
20/8/2015 06:13:55 am
Thanks Paul. Another variant may be to reflect vertically. like
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Paul
21/8/2015 12:27:12 am
So Timothy and Hare Ram are suggesting variants too! Great stuff! I wonder if anybody will take on your challenges!
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Tom
21/8/2015 05:44:08 pm
Hare Ram's variant has 16 solutions provided that the "1" has left right symmetry, but only 1 solution if it hasn't (so my answer would be 1).
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Paul
22/8/2015 12:08:00 am
Would Hare Ram like to comment on Tom's extra solution? Thanks as ever, Tom.
Hare Ram Agarwal
22/8/2015 04:40:03 am
Thanks Tom.
tom
25/8/2015 05:50:01 am
Yes, Hare Ram, you are right. I don't know where my 16 came from!
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Norris
8/9/2015 10:35:16 pm
1st digit 0,1
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Paul
9/9/2015 11:30:07 am
Thanks Norris. Maybe one of our other participants would like to verify your second solution..?
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