Try this one!

 

This puzzle is related to arithmetic...
How many times per day does a digital clock display a palindromic number?


 

 

Solution
The problem is underspecified.  Digital clocks may run from


(a) 1:00 to 12:59

(b) 01:00 to 12:59

(c) 0:00 to 23:59

(d) 00:00 to 23:59

(e-h) any of the above with seconds appended, :00 to :59.

I agree that not all of these are common, but I have seen some uncommon
ones.  For that matter, I've seen ones not on the above list -- the Toronto
subway stations used to contain digital clocks that ran from 0:00 to 12:59
(pm), then from 1:00 (pm) to 11:59 (pm), while a computer that I used to
use had the inverse anomaly -- its time of day command displayed times
from 12:00:00 to 12:59:59 (am), then 01:00:00 to 23:59:59!

I get the following results for the 8 cases.


CASE
AM+PM
HOURS pals/hr  TOTAL
OVERALL TOTAL

(a)
yes
1-9
 6
 54



10-12
 1
  3
114


(b)
yes
01-05
 1
  5



06-09
 0
  0



10-12
 1
  3
16


(c)
no
0-9
 6
 60



10-15
 1
  6



16-19
 0
  0



20-23
 1
  4
70


(d)
no
00-05
 1
  6



06-09
 0
  0



10-15
 1
  6



16-19
 0
  0



20-23
 1
  4
16


(e)
yes
1-9
60
540



10-12
 6
 18
1116


(f)
yes
01-05
 6
 30



06-09
 0
  0



10-12
 6
 18
96


(g)
no
0-9
60
600



10-15
 6
 36



16-19
 0
  0



20-23
 6
 24
660


(h)
no
00-05
 6
 36



06-09
 0
  0



10-15
 6
 36



16-19
 0
  0



20-23
 6
 24
96

--Mark Brader (msb@sq.com)

 

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