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)
Reply
Anand Mehta
19/8/2015 04:14:49 am
Only 4 digits possible: 0,1,3 and 8.
Reply
Timothy Tran
20/8/2015 04:54:49 am
Same method.
Reply
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:
Reply
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.
Reply
Hare Ram Agarwal
20/8/2015 06:13:55 am
Thanks Paul. Another variant may be to reflect vertically. like
Reply
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!
Reply
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).
Reply
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!
Reply
Norris
8/9/2015 10:35:16 pm
1st digit 0,1
Reply
Paul
9/9/2015 11:30:07 am
Thanks Norris. Maybe one of our other participants would like to verify your second solution..?
Reply
## Leave a Reply. |
## Puzzle Ideas
If you have an idea for puzzle of the month, then please do let me know. ## Archives
August 2017
Don't forget to check out 'Teach Further Maths' - PowerPoints for Teachers and Students of A-Level Further Maths ...and the brilliant NEW educational card game 'Maths Trumps' |