Monster. (1 Viewer)

[seanieg89]

A man is in the middle of a circular lake and a monster is at the edge of the shore. The monster runs around the lake at a speed X times the swimming speed of the man (but much slower than the man's running speed), and chooses his running direction at all times optimally in order to catch the man.

a) Can the man escape if X=4? Justify your answer.

b) What is the largest X such that the man can escape and outline the escape strategy for this X.

 

[kawaiipotato]

Curious for the solution. I tried it but I realised can't the man just change directions during his path?

 

[InteGrand]

Curious for the solution. I tried it but I realised can't the man just change directions during his path?

Yes, and the monster changes his too (''chooses his running direction at all times optimally in order to catch the man'').

 

[psyc1011]

This is so interesting... going to think about this tonight

 

[jonathan_lam]

Reminds me of https://www.research.ibm.com/haifa/ponderthis/challenges/May2001.html and https://www.research.ibm.com/haifa/ponderthis/solutions/May2001.html (spoiler alert - solutions are in the second link)

 

[braintic]

and chooses his running direction at all times optimally in order to catch the man

This is somewhat ambiguous. Does the monster sense a curved path and run to intercept where this curve meets the shoreline. Or does it only sense the current direction of motion?

And do we assume that X times the man's swimming speed is only the maximum speed for the monster, and that it is free to run as slow as it wants?

 

[seanieg89]

This is somewhat ambiguous. Does the monster sense a curved path and run to intercept where this curve meets the shoreline. Or does it only sense the current direction of motion?

And do we assume that X times the man's swimming speed is only the maximum speed for the monster, and that it is free to run as slow as it wants?

It has been ages since I solved this, and I did not write it myself so I cannot be 100% sure. But I believe:

1. It can only see the current position and direction of swimming, but it is also intelligent enough to plan ahead and anticipate the possible plans of the man.

2. Yes it can run as slow as it likes.

 

[anomalousdecay]

I got a really simple solution yielding .

Might be wrong though as I only took a few minutes to think about it and write it out.

Edit: is this more of a simple logic based question or a question of many variables and tedious solution?

Also, I remember the OP date being the date of our MX2 exam. That's probably why no-one answered it back then haha. Everyone was too hyped and busy talking about that exam.

 

[seanieg89]

I got a really simple solution yielding .

Might be wrong though as I only took a few minutes to think about it and write it out.

Edit: is this more of a simple logic based question or a question of many variables and tedious solution?

Also, I remember the OP date being the date of our MX2 exam. That's probably why no-one answered it back then haha. Everyone was too hyped and busy talking about that exam.

Nope, the upper bound is not close to .

Its logic based (in that it is not lateral), but I wouldn't necessarily call it simple.

I didn't use multiple variables, but there are probably lots of ways to think about it and phrase your working.

It isn't hugely tedious but it is not trivial either.

 

[kawaiipotato]

So is there a solution for this?

 

[Paradoxica]

This is a very concise solution to the problem. It also generalises the problem to arbitrarily large lakes.