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Old 2006-05-02, 10:41   #1
davar55
 
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Default The Clock Problem

A clock chimes the hour, and once on the half hour.
When she arrived home, she heard one ring.
A half hour later she heard another ring.
A half hour later she heard a third ring.
A half hour later she heard yet another ring.
And finally, a half hour later,
as she was leaving, she heard one more ring.

How is this possible, and what time did she arrive home?
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Old 2006-05-02, 11:24   #2
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Default Out the nick of time

She entered her house when the clock struck his last of twelve strikes
(this would be at approximately 12h00.33 sec(3 seconds per strike, first on the hour). Then there were three 'normal' rounds. Leaving at exactly 2 o'clock she heard the first strike, but the last escaped her. :cat:
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Old 2006-05-02, 16:25   #3
ewmayer
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She lives on a planet whose rotational period is 2 hours.
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Old 2006-05-02, 17:31   #4
axn
 
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Quote:
Originally Posted by ewmayer
She lives on a planet whose rotational period is 2 hours.
Shouldn't that be 1 hour?
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Old 2006-05-02, 18:13   #5
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Quote:
Originally Posted by axn1
Shouldn't that be 1 hour?
That would work, as well. (Think of a typical clock that cycles through the hours twice a day.)
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Old 2006-05-02, 18:34   #6
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Her clock only ever indicates that half an hour has passed since the last chime.
That is, it never chimes more than once on the hour.

This explanation meets a strict reading of the question. You only said it chimes the hour. You did not say that the number of chimes on the hour is equal to the number of hours since midnight and/or noon.

Paul
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Old 2006-05-02, 19:20   #7
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Quote:
Originally Posted by xilman
You only said it chimes the hour. You did not say that the number of chimes on the hour is equal to the number of hours since midnight and/or noon.
That occurred to me as well, but then I decided that "chimes the hour" is generally taken to mean "indicates the hour by chiming that many times *on* the hour." Basically, the standard legal "what would a hypothetical reasonable obsessive clock-watcher assume?" criterion.
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Old 2006-05-02, 20:04   #8
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Quote:
Originally Posted by davar55
I might have said, in the puzzle:
A clock chimes every hour the number of times ...
But I wanted the most succinct reply solution.
Think you can provide that?
Ah, I think we've beaten this one pretty much into moribundity.
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Old 2006-05-02, 22:13   #9
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I like it better when the clock makes noise every 15 minutes. Having someone wake up when the power is out prevents them from looking at the clock. And makes them need to know the time.
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Old 2006-05-26, 01:53   #10
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Variations on a theme: solutions to the clock problem.

The simplest answer is 12:00:00 (AM or PM).

The idea that the rotational period of the planet is
two hours, or one hour, or in fact exactly 2/n hours
where n is any positive integer, is intrigueing.
It means she could have returned home at any chime time.
Even prime chime time.

The suggestion that the clock is stuck on the half hour chime
does technically meet the conditions of the problem, but
"chimes the hour" is a concise way of saying "chimes the number
of times equal to the value of the hour". And the problem does
assume a 12-hour (not 24-hour) clock.

I was thinking of an old Grandfather clock. In the age of
digital/electronic clocks and watches and the GPSS, there
are other variations of solutions to this puzzle.

But the basic answer is: any noon or midnight (any day at all).

-- davar55
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