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Math Puzzle: Lion in Circular Cage Puzzle

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Re: Math Puzzle: Lion in Circular Cage Puzzle

#21

Post by yogsototh »

screwt wrote: post #19

Assuming both players react instantaneously, and space is modelled as continuous (not discrete), I think the following strategy always wins for the lion. 1. Lion runs to centre of ring 2. Lion moves toward tamer, but always staying directly between tamer and centre. (2) is always possible, as the arc the lion has to move around to keep between tamer and centre is always shorter than any arc the tamer can move along s…

I believe it works only if the Lion and the tamer have a non null size (not represented as point). I am not sure of this, but if you represent the Lion and the tamer as points, the Lion can go as close as it want to the tamer, but never really reach him. Of course considering the tamer is on the border.

Re: Math Puzzle: Lion in Circular Cage Puzzle

#22

Post by nonce43 »

tylerneylon wrote: post #9

This is a problem you can be sure you've solved, only to find a twist in the road. It's problem 1 in The Art of Mathematics by Béla Bollobás, a challenging puzzle book for serious math junkies. The solution in that book has a good explanation of (a) what you probably didn't think of, and sounds right; and (b) why it's wrong. And just when you think Bollobás's book had the final word, you found out there are versions…

The above link pretty much answers everything. Please, skim the first two pages before replying. It explains why 'curve of pursuit' is the wrong strategy, how the lion can win if the tamer stays on the circumference, why the tamer should not stay on the circumference, and how to make this all mathematically rigorous.

Re: Math Puzzle: Lion in Circular Cage Puzzle

#23

Post by yogsototh »

ranit8 wrote: post #20
tylerneylon wrote: post #9

This is a problem you can be sure you've solved, only to find a twist in the road. It's problem 1 in The Art of Mathematics by Béla Bollobás, a challenging puzzle book for serious math junkies. The solution in that book has a good explanation of (a) what you probably didn't think of, and sounds right; and (b) why it's wrong. And just when you think Bollobás's book had the final word, you found out there are versions…

Sorry, i'm too lazy to deeply check teh article. What happens if the lion starts from the center and always moves as to keep the center, himself and the tamer in a straight line? It should do some kind of spiral, but does it take infinite time to catch the tamer? EDIT: someone came just before me. http://news.ycombinator.com/item?id=3617030

I believe the Lion can go as close as he wants to the tamer but never have both the same position. If you consider the Lion and the tamer have a size, then in a finite time, the Lion reach the tamer.

Re: Math Puzzle: Lion in Circular Cage Puzzle

#24

Post by screwt »

ranit8 wrote: post #20
tylerneylon wrote: post #9

This is a problem you can be sure you've solved, only to find a twist in the road. It's problem 1 in The Art of Mathematics by Béla Bollobás, a challenging puzzle book for serious math junkies. The solution in that book has a good explanation of (a) what you probably didn't think of, and sounds right; and (b) why it's wrong. And just when you think Bollobás's book had the final word, you found out there are versions…

Sorry, i'm too lazy to deeply check teh article. What happens if the lion starts from the center and always moves as to keep the center, himself and the tamer in a straight line? It should do some kind of spiral, but does it take infinite time to catch the tamer? EDIT: someone came just before me. http://news.ycombinator.com/item?id=3617030

There's an alternate strategy that relies on time moving in discrete chunks, and both players moving simultaneously. But it's completely dependent on how the space is modelled, which indicates (to me) that this isn't a satisfying / robust / realistic solution.

Re: Math Puzzle: Lion in Circular Cage Puzzle

#25

Post by andrewingram »

tylerneylon wrote: post #9

This is a problem you can be sure you've solved, only to find a twist in the road. It's problem 1 in The Art of Mathematics by Béla Bollobás, a challenging puzzle book for serious math junkies. The solution in that book has a good explanation of (a) what you probably didn't think of, and sounds right; and (b) why it's wrong. And just when you think Bollobás's book had the final word, you found out there are versions…

28 pages and not a single diagram. This is why I always struggled reading academic papers.

For a problem like this when the first thing I did was have a picture of it in my head, I would have expected diagrams to be essential.

Re: Math Puzzle: Lion in Circular Cage Puzzle

#27

Post by tomelders »

I hate questions being phrased like this. I always end up thinking of things like "who entered the cage first", which is important in reality but has no bearing on the mathematical nature of the question.

If the lion tamer is in the cage before when the lion enters, then it's unlikely the that the Lion will catch the tamer. Unless there's some other factor, like the lion has been starved, or is nervous.

Re: Math Puzzle: Lion in Circular Cage Puzzle

#28

Post by shpoonj »

philbarr wrote: post #26

Mathematics aside, is this one of those puzzles where the answer is "of course the lion tamer is not caught - because he's a lion tamer and therefore the lion does not chase him."

There are many holes in the question... Such as asking if it is POSSIBLE. We know that all things are possible, however improbable, so the answer is yes.

Re: Math Puzzle: Lion in Circular Cage Puzzle

#30

Post by hythloday »

zackzackzack wrote: post #2

For those curious about the mathematical objects involved: http://mathworld.wolfram.com/PursuitCurve.html https://en.wikipedia.org/wiki/Pursuit_curve If you model this, you will probably get very different answers based on how well you discrete-ize (is there a better word for that idea?) the time and movement. Also, it's not a turn based game, i.e. the man doesn't move and then the lion moves. They move together at t…

is there a better word for that idea?

Quantize. :)

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