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

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Guest Message by DevFuse

Started by bonanova, Nov 24 2013 08:37 AM

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

18 replies to this topic

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.

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?

*Vidi vici veni.*

Posted 25 November 2013 - 12:30 AM

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

*Vidi vici veni.*

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." )

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." )

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.

*Vidi vici veni.*

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.

Past prime, actually.

Posted 25 November 2013 - 08:53 PM

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

Spoiler for but

*Vidi vici veni.*

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.**

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

Past prime, actually.

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?.

*Vidi vici veni.*

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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