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48 arithmetic/clock/palindromic.p




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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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