20060502, 10:41  #1 
May 2004
New York City
5·7·11^{2} 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? 
20060502, 11:24  #2 
Dec 2005
11000100_{2} 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: 
20060502, 16:25  #3 
∂^{2}ω=0
Sep 2002
Repรบblica de California
11,743 Posts 
She lives on a planet whose rotational period is 2 hours.

20060502, 17:31  #4  
Jun 2003
2^{2}·7·193 Posts 
Quote:


20060502, 18:13  #5  
∂^{2}ω=0
Sep 2002
Repรบblica de California
11,743 Posts 
Quote:


20060502, 18:34  #6 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
7·31·53 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 
20060502, 19:20  #7  
∂^{2}ω=0
Sep 2002
Repรบblica de California
10110111011111_{2} Posts 
Quote:


20060502, 20:04  #8  
∂^{2}ω=0
Sep 2002
Repรบblica de California
11,743 Posts 
Quote:


20060502, 22:13  #9 
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
2^{2}·3·5·179 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.

20060526, 01:53  #10 
May 2004
New York City
5×7×11^{2} 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 12hour (not 24hour) 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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