The Clock Problem

davar55 · 2006-05-02, 10:41

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?

Kees · 2006-05-02, 11:24

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:

ewmayer · 2006-05-02, 16:25

She lives on a planet whose rotational period is 2 hours.

axn · 2006-05-02, 17:31

Quote:

Originally Posted by ewmayer

She lives on a planet whose rotational period is 2 hours.

Shouldn't that be 1 hour?

ewmayer · 2006-05-02, 18:13

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.)

xilman · 2006-05-02, 18:34

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

ewmayer · 2006-05-02, 19:20

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.

ewmayer · 2006-05-02, 20:04

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.

Uncwilly · 2006-05-02, 22:13

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.

davar55 · 2006-05-26, 01:53

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

2006-05-02, 10:41	#1
davar55 May 2004 New York City 5×7×11² Posts	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?

2006-05-02, 11:24	#2
Kees Dec 2005 2²·7² Posts	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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2006-05-02, 16:25	#3
ewmayer ∂²ω=0 Sep 2002 República de California 19·613 Posts	She lives on a planet whose rotational period is 2 hours.

2006-05-02, 18:34	#6
xilman Bamboozled! "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 2×5,393 Posts	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

2006-05-02, 22:13	#9
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 9844₁₀ Posts	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.

2006-05-26, 01:53	#10
davar55 May 2004 New York City 4235₁₀ Posts	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