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An "Oldie" with a twist of lemon


Best Answer Prime, 22 February 2013 - 02:08 AM

I have a cold, my head is stuffed, I feel like an Ogre. I am not figuring out the differential equations to deny hungry Ogre his meal. However, here is some food for thought for those Brain Denizens who took the maiden's side. Indeed, she could go slower. Mayhap, someone will try carrying out the required calculations, make an error and give the maiden a wrong advice.

Spoiler for maiden voyage

To make the contest fair, the maiden should have only so much time for rowing. Having exhausted it, she falls asleep. Whereafter, the Ogre should start blowing at the boat pushing it towards the shore...

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49 replies to this topic

#1 bonanova

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Posted 20 February 2013 - 09:30 PM

An ogre with a top land  speed of 4 mph, but incapable of swimming, stalks the shore of a circular lake. The fair maiden out in the boat can outrun the ogre on land, but her rowing speed is nothing to write home to mother about. How fast must she be able to row to effect an escape?

 

Make the assumption that the ogre is hungry [or otherwise desirous of the girl] and uses a best-strategy pursuit.


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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 ThunderCloud

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Posted 20 February 2013 - 10:00 PM

Spoiler for


Edited by ThunderCloud, 20 February 2013 - 10:01 PM.

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#3 CaptainEd

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Posted 20 February 2013 - 10:17 PM

Spoiler for smart maiden outwits ogre!


Edited by CaptainEd, 20 February 2013 - 10:21 PM.

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#4 ThunderCloud

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Posted 20 February 2013 - 10:44 PM

Spoiler for smart maiden outwits ogre!

Drat! You're right...

Spoiler for


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#5 Prime

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Posted 20 February 2013 - 10:48 PM

Spoiler for a good exercise

Nice problem.


Edited by Prime, 20 February 2013 - 10:53 PM.

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Past prime, actually.


#6 CaptainEd

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Posted 20 February 2013 - 11:02 PM


Spoiler for smart maiden outwits ogre!

Drat! You're right...

Spoiler for

Drat! You're right...I thought she could certainly spiral her way out. But a sufficiently slow-paddling maiden could actually be driven back into the center. Trickier than I thought, too.


Edited by CaptainEd, 20 February 2013 - 11:06 PM.

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#7 bonanova

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Posted 21 February 2013 - 12:32 AM

Spoiler for a good exercise

Nice problem.

 

Are you sure she has to row that fast?


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#8 Prime

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Posted 21 February 2013 - 01:03 AM

 


Spoiler for a good exercise

Nice problem.

 

Are you sure she has to row that fast?

The question in the OP is: "How fast she must she be able to row..." (meaning top speed.)

Spoiler for not to say


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Past prime, actually.


#9 Prime

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Posted 21 February 2013 - 01:14 AM

Spoiler for On second thought,


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Past prime, actually.


#10 bonanova

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Posted 21 February 2013 - 04:37 AM

We have a sufficient condition.

Escape is possible if the ogre's speed ratio advantage is not greater than [ 1 + pi  ].

 

Is it also an necessary condition?

I.e. can she escape if the speed ratio is higher?  How much higher?

 

That's the "twist" mentioned in the title. ;)


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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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