49 replies to this topic

[Yoruichi-san]

I think I need a clarification on "best-strategy pursuit".  Does this mean the ogre will move towards/wait at the point in the circle that is closest to the maiden's current position?  Or does it mean it will try to 'follow' the maiden based on her current trajectory?  

[bonanova]

I think I need a clarification on "best-strategy pursuit".  Does this mean the ogre will move towards/wait at the point in the circle that is closest to the maiden's current position?  Or does it mean it will try to 'follow' the maiden based on her current trajectory?  

 

The ogre will try to be on the shore where the boat lands before the boat gets there. It is a game. Whoever gets to that point first wins. The rower and ogre each act in their own best interest. The rest is part of the puzzle. The rower can row anywhere on the lake and the ogre can run anywhere on the shore. Assume each can turn on a dime [infinite acceleration, maximum speed.]

 

Best strategy pursuit means to imply that the ogre will not lie down and take a nap.

 

And the specific question now is Can the rower overcome a ogre speed ratio of greater than (1 + pi)?.

[Yoruichi-san]

Right, it is a game...and when it comes to games there's the whole trying to outguess your opponent part...

 

Spoiler for A tricksy maiden

Since the maiden's motion is not constrained to smooth curves and is not constrained to a constant velocity?, it's pretty hard for the ogre to guess her landing point and/or time.  She could row to, like, just out of grabbing distance of one edge, and then 'feint' accelerating movement towards the opposite edge, wait til the Ogre gets to her apparent landing point, then make a mad dash towards her original point, etc.  

 

If the Ogre fell for the feint, and thinks she's going to land on the opposite edge, it's in his best interest to move in that direction as quickly as he needs to catch up with her apparent acceleration, but if he thinks she might go in a different direction or stop accelerating, it's in his best interest to move at a slower rate, and if he thinks she's going to make a mad dash back to the closest point on the circle, it's in his best interest to stay where he is.    

[bonanova]

Wow ... in puzzles as in life.   

[Prime]

I was developing a winning strategy for the Ogre based on the inertia of the boat. But then Bonanova added an infinite acceleration.

Spoiler for more geometry for maiden

Once outside her small circle perimeter, maiden can no longer keep the center of the lake between herself and Ogre. However, she could point the nose of her boat to the point opposite Ogre. As long as she still approaches the shore. Would that help?

If maiden went at an angle, would she increase her distance at lesser rate than Ogre's?

What if maiden zig-zagged her boat pointing to the left and right of the point on the shore opposite to the Ogre's position? I hope the Ogre is smart enough to ignore the direction where maiden goes and head to the point on the shore closest to her boat.

Either way, the Ogre is at disadvantage. Whenever maiden feels she is not making it, she could always turn back to the center of the lake. Ogre should try and woe her instead of chasing.

Edited by Prime, 21 February 2013 - 07:41 AM.

[bonanova]

I was developing a winning strategy for the Ogre based on the inertia of the boat. But then Bonanova added an infinite acceleration.

Spoiler for more geometry for maiden

Once outside her small circle perimeter, maiden can no longer keep the center of the lake between herself and Ogre. However, she could point the nose of her boat to the point opposite Ogre. As long as she still approaches the shore. Would that help? OgreMaiden.gifIf maiden went at an angle, would she increase her distance at lesser rate than Ogre's?What if maiden zig-zagged her boat pointing to the left and right of the point on the shore opposite to the Ogre's position? I hope the Ogre is smart enough to ignore the direction where maiden goes and head to the point on the shore closest to her boat.Either way, the Ogre is at disadvantage. Whenever maiden feels she is not making it, she could always turn back to the center of the lake. Ogre should try and woe her instead of chasing.

This looks promising. How much advantage might be gained?

[CaptainEd]

Actually, you folks have convinced me that

Spoiler for quick Denizens outwit slow Captain!

aiming at the spot on the other end of O's current diameter is very suboptimal. Prime's original proposal of having M head towards the closest spot on shore (after moving to the far side of M's orbit) is almost optimal. I have the feeling that there's some real-time adjustment that M can/should make, but they still involve aiming at the nearest spot where M can get to before O can get there. It feels very much like a book I marveled at years ago, called Differential Games. I fear that Diff Eq is required, which means I'll be simulating with Excel, if I'm so lucky.

[TimeSpaceLightForce]

Spoiler for

The ogre will try to be on the shore where the boat lands before the boat gets there.

The lady get as near the ogre as she can be..face to face. Then at slowest speed start rowing backward

until the ogre is at her back.Then full speed ahead.

[CaptainEd]

Spoiler for preliminary results

even if M speed is slightly less than the breakeven speed O/(1+pi), M can benefit from a slight course correction, once O has made a commitment. So, assume M follows Prime recommendation, and starts at the far side of M's smaller circle, heading directly away from O. O chooses a direction (CW or CCW) and hustles around. If M's speed is 99% of break even, M can wait until O has gone as much as 90% of the way around, and then change course several degrees, and reach shore before O arrives. The slower M is, the earlier she must make this correction. In my simulation, I found that if M is slower than 95% of break even, there is no such correction possible. I don't see what is special about 95, so I'm a little doubtful of my analysis.

[bonanova]

Spoiler for preliminary results

even if M speed is slightly less than the breakeven speed O/(1+pi), M can benefit from a slight course correction, once O has made a commitment. So, assume M follows Prime recommendation, and starts at the far side of M's smaller circle, heading directly away from O. O chooses a direction (CW or CCW) and hustles around. If M's speed is 99% of break even, M can wait until O has gone as much as 90% of the way around, and then change course several degrees, and reach shore before O arrives. The slower M is, the earlier she must make this correction. In my simulation, I found that if M is slower than 95% of break even, there is no such correction possible. I don't see what is special about 95, so I'm a little doubtful of my analysis.

 

Good Job, Cap'n, you've lowered the bar for M, giving her time for a little
touch-up for the reporters sure to be at the shore covering the story
for CNN.

 

Can you go beyond 5%?