Description
This article is from the Puzzles FAQ,
by Chris Cole chris@questrel.questrel.com and Matthew Daly
mwdaly@pobox.com with numerous contributions by others.
48 arithmetic/clock/palindromic.p
How many times per day does a digital clock display a palindromic number?
arithmetic/clock/palindromic.s
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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