How many times per day does a digital clock display a palindromic number?

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)