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Guest Message by DevFuse

Of dogs and men

19 replies to this topic

#1 bonanova

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Posted 16 April 2013 - 08:21 AM

An old Sam Lloyd classic that has to be dusted off every now and again. It's deceptively simple, and more fun to solve than to Google.

Enjoy.

A square phalanx of soldiers, 100 feet on a side, marches forward at a constant speed. The company mascot, a small terrier, trots along with them, starting at the center of the rear rank. Since he moves more quickly than the soldiers, he is able to trot at constant speed around the outside of the square, keeping as close as possible to the soldiers at all times. When he returns to his starting position at the rear of the formation, the soldiers have moved forward a distance of 50 feet. How long is the dog's path?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 caike

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Posted 16 April 2013 - 11:23 AM

I think the answer for the length of the dog's path could be 50*sqrt(65) feet.

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#3 bhramarraj

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Posted 16 April 2013 - 11:56 AM

Spoiler for

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#4 caike

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Posted 16 April 2013 - 12:21 PM

I think the answer for the length of the dog's path could be 50*sqrt(65) feet.

Sorry, I think I am wrong...

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#5 k-man

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Posted 16 April 2013 - 03:35 PM

Spoiler for estimate at a first glance

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#6 k-man

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Posted 16 April 2013 - 05:37 PM

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#7 bonanova

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Posted 16 April 2013 - 11:12 PM

Spoiler for

Spoiler for Not given but relatively implied

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#8 bonanova

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Posted 16 April 2013 - 11:13 PM

I think the answer for the length of the dog's path could be 50*sqrt(65) feet.

Sorry, I think I am wrong...

Not far off, but it's more complex than that.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 bonanova

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Posted 16 April 2013 - 11:14 PM

Spoiler for Close

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#10 bonanova

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Posted 17 April 2013 - 08:26 AM

Clue:

There is an algebraic solution (closed form) and a trigonometric solution (numerical.)

Spoiler for I like the trig solution - it's less messy.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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