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A lion and its tamer


Best Answer Grimbal, 30 November 2013 - 03:02 AM

Spoiler for If the tamer runs on the perimeter

 

Spoiler for If the tamer is not on the perimeter
 
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18 replies to this topic

#1 bonanova

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Posted 24 November 2013 - 08:37 AM

A while back, we had fun rescuing a fair maiden in a boat on a circular lake from a dog.
Here's another circular chase problem, but this time it's in a cage.
 
A lion and its tamer are inside a circular cage of radius 1.
They both can run effortlessly at a top speed of 1.
  • If the lion gets hungry, does the tamer become his lunch?
  • If so, what's the longest time the tamer has to live?
Since this is a puzzle, they both can be represented as points.
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#2 bonanova

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Posted 25 November 2013 - 12:30 AM

The lion begins to pace; the tamer stands to his feet and looks nervously to his left.


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#3 plasmid

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Posted 25 November 2013 - 04:08 AM

Should we assume the lion will always run straight for the trainer, or can the lion do whatever it feels is an optimal strategy? (I get the feeling the answer might be "calculate it both ways.")

And should we consider a starting position where the trainer is at the edge of the cage and the lion is in the center, or something else? (At least with this question you can't reasonably say "calculate it for all possible starting positions." ^_^)
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#4 bonanova

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Posted 25 November 2013 - 09:04 AM

Lion is not constrained. He wants to eat.

Tamer does not want to be eaten.

 

Starting positions could be opposite ends of diameter.

After one unit of time lion could be at the center; tamer maintains maximum separation by not moving.

We can start the chase from there.


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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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#5 Prime

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Posted 25 November 2013 - 06:03 PM

I be the Lion.

Spoiler for My strategy for catching trainers

There. Someone solve it for me.

 

BTW, it was an Ogre last time, not a dog.

 


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Past prime, actually.


#6 bonanova

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Posted 25 November 2013 - 08:53 PM

I be the Lion.

Spoiler for My strategy for catching trainers

There. Someone solve it for me.
 
BTW, it was an Ogre last time, not a dog.

Right. An ogre. It was a dog and rabbit.

Spoiler for but

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#7 plasmid

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Posted 26 November 2013 - 04:00 PM

I was thinking along the same lines as Prime as far as the lion's strategy. But based on this calculation, that might not be a viable approach.
Spoiler for What I've got so far

Edited by plasmid, 26 November 2013 - 04:04 PM.

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#8 Prime

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Posted 26 November 2013 - 06:29 PM

Why should a hungry lion devise the best strategy of escape for a tasty tamer?

Spoiler for the lion must eat

 


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Past prime, actually.


#9 bonanova

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Posted 28 November 2013 - 10:25 AM

I was thinking along the same lines as Prime as far as the lion's strategy. But based on this calculation, that might not be a viable approach.

Spoiler for What I've got so far

 

You are right about the lion's radial speed - it's faster than your approximation.

 

Does the lion catch the tamer?.


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#10 Grimbal

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Posted 30 November 2013 - 03:02 AM   Best Answer

Spoiler for If the tamer runs on the perimeter

 

Spoiler for If the tamer is not on the perimeter
 

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