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Topic: Exchanging Hands (Read 645 times) |
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william wu
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Exchanging Hands
« on: Feb 17th, 2003, 9:24pm » |
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"If the hour and minute hands of a watch are interchanged, how many different possible times could the watch show?"
- Source: Engineering News (ucb)
I want to say the "obvious" answer, but this is supposed to be a brainteaser so I might have missed something. Thought I'd see what you guys think.
P.S. I'm slowly in the process of databasing the site now, so sorry about the lack of updates recently.
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| « Last Edit: Feb 17th, 2003, 9:28pm by william wu » |
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aero_guy
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Re: Exchanging Hands
« Reply #2 on: Feb 18th, 2003, 10:14am » |
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what do you mean by times? Do mean instances where the minute and hour hands are in the correct places for a specific time? If so, I think towr has it.
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william wu
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Re: Exchanging Hands
« Reply #3 on: Feb 18th, 2003, 10:19am » |
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I thought the problem was asking: how many unique configurations of hour and minute hands exist? Although I can't be certain since I'm just quoting the author.
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James Fingas
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Re: Exchanging Hands
« Reply #4 on: Feb 18th, 2003, 11:05am » |
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It seems to me that your 11 solutions fit into a broader set of solutions. For instance:
When the hour hand is at 15.105 minutes after noon, and the minute hand is at 15.105 minutes past the hour. If you change the hands, the hour hand is at 1.259 minutes past three, and the minute hand is at 1.259 minutes past the hour.
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Doc, I'm addicted to advice! What should I do?
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poseur
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Wouldn't you hit a valid time 11 times every hour?
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TimMann
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Re: Exchanging Hands
« Reply #6 on: Feb 20th, 2003, 1:47am » |
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If aero_guy's interpretation is correct, the puzzle is the same as Analog Clock III in the medium section. There's a solution in the medium forum.
If William's interpretation is correct, then if the hands move continuously, there are an uncountable infinity of positions they can be in, same as if you didn't swap them. Is that what you meant? It seems pretty trivial.
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william wu
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Re: Exchanging Hands
« Reply #7 on: Mar 9th, 2003, 4:15am » |
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Yes, it turns out that aero_guy's interpretation is correct, so it's just like Analog Clock III (correct answer is 143 times in a day ). I should've known better than to think the puzzle would be simple.
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