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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

#21 phaze

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Posted 21 February 2013 - 11:59 PM

Spoiler for smart maiden outwits ogre!

Spoiler for Wouldn't it be..


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#22 CaptainEd

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Posted 22 February 2013 - 12:42 AM

Yes, phaze, I was way off base.

Spoiler for fuzzy thoughts

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#23 Prime

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Posted 22 February 2013 - 02:08 AM   Best Answer

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...


Edited by Prime, 22 February 2013 - 02:09 AM.

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Past prime, actually.


#24 Yoruichi-san

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Posted 22 February 2013 - 02:12 AM

Spoiler for Are you maiden or uber-maiden?


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Women are definitely stronger. We are [Fe]males, after all...

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#25 bonanova

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Posted 22 February 2013 - 02:32 AM

Prime has got the answer, at least as far as I have analyzed it.

That being true, I will post my analysis and people can take pot shots at improving it.

 

Spoiler for On a tangent


Edited by bonanova, 22 February 2013 - 05:38 AM.
Giving proper attribution to Prime

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#26 Prime

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Posted 22 February 2013 - 03:01 AM

Phaze has got the answer, at least as far as I have analyzed it.

That being true, I will post my analysis and people can take pot shots at improving it.

 

Spoiler for On a tangent

Tangential escape does not seem the optimal even for the straight line escapes. The straight line escape with a 45-degree angle seems to perform better.


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Past prime, actually.


#27 CaptainEd

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Posted 22 February 2013 - 04:37 AM

Spoiler for doubting Ogre gives up so quick

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#28 Prime

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Posted 22 February 2013 - 05:15 AM

Spoiler for doubting Ogre gives up so quick

 

It is a lot simpler than that for the zen master Ogre. The Ogre ignores where the maiden looks, where she goes, and where she intends to go. Ogre simply draws an imaginary straight line from the center of the lake, through the boat, to the shore; and heads for that spot using the shorter arch. Insofar as the optimum is concerned, it is the Ogre who determines the path -- not the maiden. The maiden reacts to Ogre's moves, not other way around.

If the maiden wanders back into her inner circle r, that could make the Ogre change the direction when the boat crosses straight line drawn from the Ogre to the center of the lake. Then the young lady would be going towards Ogre rather than away from him. (Not an optimal strategy.)

Presently, we are solving the sub-problem, where the maiden after leaving her inner circle goes in a straight line towards some point on the shore. We must find, that point. Bonanova suggested going off the inner circle on a tangent line. That gives a better ratio than going in a straight line to the nearest point on the shore. However, I don't believe it is the optimum.

The numbers I have given in the post #23 inside the spoiler are off. But then, as everyone knows, I am siding with Ogre.


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Past prime, actually.


#29 bonanova

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Posted 22 February 2013 - 05:20 AM


Spoiler for doubting Ogre gives up so quick

 

It is a lot simpler than that for the zen master Ogre. The Ogre ignores where the maiden looks, where she goes, and where she intends to go. Ogre simply draws an imaginary straight line from the center of the lake, through the boat, to the shore; and heads for that spot using the shorter arch. Insofar as the optimum is concerned, it is the Ogre who determines the path -- not the maiden. The maiden reacts to Ogre's moves, not other way around.

If the maiden wanders back into her inner circle r, that could make the Ogre change the direction when the boat crosses straight line drawn from the Ogre to the center of the lake. Then the young lady would be going towards Ogre rather than away from him. (Not an optimal strategy.)

Presently, we are solving the sub-problem, where the maiden after leaving her inner circle goes in a straight line towards some point on the shore. We must find, that point. Bonanova suggested going off the inner circle on a tangent line. That gives a better ratio than going in a straight line to the nearest point on the shore. However, I don't believe it is the optimum.

The numbers I have given in the post #23 inside the spoiler are off. But then, as everyone knows, I am siding with Ogre.

 

Blame it on the cold, Prime. ;)

 

I am not convinced that tangential is optimal - it may not be enough!

It's easy to overlook that r is one of the unknowns.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#30 Prime

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Posted 22 February 2013 - 05:26 AM

 


Spoiler for doubting Ogre gives up so quick

 

It is a lot simpler than that for the zen master Ogre. The Ogre ignores where the maiden looks, where she goes, and where she intends to go. Ogre simply draws an imaginary straight line from the center of the lake, through the boat, to the shore; and heads for that spot using the shorter arch. Insofar as the optimum is concerned, it is the Ogre who determines the path -- not the maiden. The maiden reacts to Ogre's moves, not other way around.

If the maiden wanders back into her inner circle r, that could make the Ogre change the direction when the boat crosses straight line drawn from the Ogre to the center of the lake. Then the young lady would be going towards Ogre rather than away from him. (Not an optimal strategy.)

Presently, we are solving the sub-problem, where the maiden after leaving her inner circle goes in a straight line towards some point on the shore. We must find, that point. Bonanova suggested going off the inner circle on a tangent line. That gives a better ratio than going in a straight line to the nearest point on the shore. However, I don't believe it is the optimum.

The numbers I have given in the post #23 inside the spoiler are off. But then, as everyone knows, I am siding with Ogre.

 

Blame it on the cold, Prime. ;)

 

I am not convinced that tangential is optimal - it may not be enough!

It's easy to overlook that r is one of the unknowns.

I did overlook that r is one of the unknowns because of cold and my partiality to Ogre's cause.

Still I don't see that the problem is solved even for a straight line escape.

By the way, I did not see the answer by Phaze to which you referred. Is BD not displaying some of the posts to me?


Edited by Prime, 22 February 2013 - 05:27 AM.

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Past prime, actually.





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