NY Times math problem

Virgil wrote:

KBH wrote:

Well the speeds are fixed and the rabbit needs a particular postion on its circle...as it hunts for that circle which rotates with the agent movement.

Virgil wrote:

Reply to
KBH
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KBH wrote:

The rabbit does not know anyth> Agent strategy:

Reply to
KBH

Since the rabbit only needs to keep rack of that diameter of the pond passing through the Agent, and the pond itself does not rotate, I have no idea what rotating circle you are talking about.

Whether a rabbit or a duck, the issue is not whether it knows how to escape but whether it can escape under the given conditions. And my analysis shows that it can.

But if it were a wise duck it could merely float at the center of the pond forever, whereas a rabbit would have to keep swimming to keep its head above water.

Reply to
Virgil

The issue is not whether the rabbit knows how to escape but whether it can escape if it acts correctly. And the following shows it can.

Reply to
Virgil

If the rabbit also knows the direction to the nearest shore. adopt the following strategy (which does not involve calculation):

Step 1.

a: Keep "rotating with a radial to the agent" b: if not using maximum speed for a: turn toward the nearest shore until using maximum speed. c: continue until not approaching the nearest shore

Step 2.

a: Swim directly toward the nearest shore at maximum speed.

This will allow the rabbit to escape given any agent strategy if the agent's top speed is less than (pi+1) times the rabbit's (a slightly more complex strategy for step 2, also involving no calculation, can improve this a little).

- William Hughes

Reply to
William Hughes

William Hughes wrote:

KBH wrote:

Okay the rabbit's name is Duck...

The speeds are fixed but since the agent can stop maybe I should allow Duck to slow down. But when they sprint just say that both increase speed at the same percentage so that it's not necessary to allow for increased speed of a sprint...over their given rates.

But I'm not allowing Duck to know where 1/4 radius distance is as some point in the water. I'm only allowing Duck to know whether or not he is rotating with the agent...and that finds the break point.

Reply to
KBH

If you mean that Duck can tell when it cannot get any farther from the agent and still stay on the same diameter I concur.

Reply to
Virgil

I think we should stay with the fixed speeds...

We just find them in motion. The agent can't stop but can reverse direction. And don't worry about sprint speeds as both speeds could increase at the same rate...

Reply to
KBH

We just find them in motion...

And allowing the agent to reverse direction is just to eliminate the strategy that I wrote the computer program for. Then Duck can find rotation with the agent by spiraling outward but must also maneuver to be on the point on the other side of the radius from the agent.

Reply to
KBH

They would eventually end up together as was originally claimed.

Just like a spinning cylinder in space will eventually develop a wobble, and will eventually end up spinning end over end.

Not if the rabbit determines where their parting line is located.

Reply to
Archimedes' Lever

The rabbit will ALWAYS use his peripheral vision to determine the agent's position, and will always swim away from that attempt at capture.

They have over 270 degrees of vision without even turning their head.

Reply to
Archimedes' Lever

No. What he said is 100% true. Also, the rabbit is doing the exact opposite. i.e Trying to maximize the distance between himself and the agent.

The rabbit will win eventually, and he only needs to wait until the agent is *near* the 180 degree point. He doesn't have to get him there exactly.

Reply to
Archimedes' Lever

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Why are we constraining outselves to the rabbit moving in a spiral or along the radius of a circle? Could there not be a solution where the rabbit moves in an elliptical path, allowing the agent to gain and lose ground relative to the rabbit until the rabbit finds itself opposite the agent, but closer to the edge than a circular path would bring it?

--riverman

Reply to
riverman

the dumb bunny will never leave the pool.

Reply to
Jasen Betts

The rabbit does need to position himself exactly on the opposite side of the diameter from the agent if he expects to escape when the agent is running the fastest he can for the rabbit to escape, if both use optimal strategies.

Assuming that the rabbit starts at the center and that the agent is running at full speed, the rabbit can remain on the diameter through the agent reach the furthest radius at which his angular rate equals that of the agent while the agent travels 90 degrees around the pond.

Dave

Reply to
Dave

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When the rabbit is further from the center than a circular path would take it, its angular velocity is necessarily less than that of the agent, so the agent is decreasing the angle, and therefore the rabbit cannot catch up to the opposite side of the diameter through the agent.

Dave

Reply to
Dave

I solved it using brain No Calculus needed.

Bye Sanny

Enjoy & Chat:

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Reply to
Sanny

Me too. I just shot the damn thing. Then a 'gator ate it.

--
You can\'t have a sense of humor, if you have no sense!
Reply to
Michael A. Terrell

There is no rabbit/duck "elliptical" strategy which is as good as the one being questioned when the agent pursues an optimal strategy.

Reply to
Virgil

Stupid link for something I will NOT sign up for. Post your solution, dingledorf. This IS the discussion group.

Reply to
Archimedes' Lever

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