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Friday Puzzle -- Hickory Dickory Dock

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Friday Puzzle -- Hickory Dickory Dock

#1

Friday Puzzle -- Hickory Dickory Dock

Alex Y

You know the rhyme, but as Paul Harvey would say, this is the rest of the story.

The clock the mouse ran up was atop city hall. It was a traditional 12-hour analog clock with hour, minute, and second hands, all of which moved smoothly.

It was 12:01 p.m when the mouse got to the top, and he proceeded to jump onto the hour hand and hold on. When the minute hand was next perfectly aligned with the hour hand, he jumped to the minute hand and held on there. When the minute hand and hour hand were aligned again, he jumped back. He continued jumping back and forth each time the two were aligned until eventually all three hands were aligned, at which point he jumped off the clock.

How long did he spend on the minute hand?

Re: Friday Puzzle -- Hickory Dickory Dock

#2

P.S.

Alex Y

The clock's strike mechanism is broken, so what the poem says happened when the clock struck one didn't affect this puzzle. ;)

Re: Friday Puzzle -- Hickory Dickory Dock

#3

Re: Friday Puzzle -- Hickory Dickory Dock

Larry Barrett

To solve this you have to think back to Algebra 1 class (a long time ago), when you asked your Mom or Dad to help you figure out clock problems; if you were lucky, they could think back to when they asked their Mom or Dad to help with clock problems.

I think this is what my Dad would have said. If T is the total time before the mouse jumps off the clock, then the time the mouse sat on the minute hand = .455T.

Re: Friday Puzzle -- Hickory Dickory Dock

#4

Your dad was pretty smart

Alex Y

Correct, to the number of decimal places given.

We'll leave it at that for a while in case others are interested in working on it. Then you can explain.

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