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        riddles >> easy >> Exchanging Hands
        
(Message started by: william wu on Feb 17^th, 2003, 9:24pm)

Title: Exchanging Hands
Post by william wu on Feb 17^th, 2003, 9:24pm

"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.

Title: Re: Exchanging Hands
Post by towr on Feb 18^th, 2003, 12:59am

there are at least [hide]eleven[/hide].

Title: Re: Exchanging Hands
Post by aero_guy on Feb 18^th, 2003, 10:14am

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.

Title: Re: Exchanging Hands
Post by william wu on Feb 18^th, 2003, 10:19am

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.

Title: Re: Exchanging Hands
Post by James Fingas on Feb 18^th, 2003, 11:05am

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.

Title: Re: Exchanging Hands
Post by poseur on Feb 18^th, 2003, 11:52am

Wouldn't you hit a valid time 11 times every hour?

Title: Re: Exchanging Hands
Post by TimMann on Feb 20^th, 2003, 1:47am

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.

Title: Re: Exchanging Hands
Post by william wu on Mar 9^th, 2003, 4:15am

Yes, it turns out that aero_guy's interpretation is correct, so it's just like Analog Clock III (correct answer is [hide] 143 times in a day [/hide] ). I should've known better than to think the puzzle would be simple.