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Topic: Fox VS Duck Variation (Read 672 times) |
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chetangarg
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Fox VS Duck Variation
« on: Jul 5th, 2007, 10:17am » |
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sorry search a lot but was unable to find the thread for this one.
A fox and a rabbit are restricted to move in a circular land of given radius. They can't cross the circumference and have the same speed. Can the fox catch the rabbit.? their initial positions are unknown.
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JiNbOtAk
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Re: Fox VS Duck Variation
« Reply #1 on: Jul 5th, 2007, 7:00pm » |
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on Jul 5th, 2007, 10:17am, chetangarg wrote:Can the fox catch the rabbit?
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Depends, is the fox trying to catch the rabbit, or the duck ? 
However, if they have the same speed, I don't see how the fox could catch up, unless they are running towards each other. Or initially, the fox already caught up, which would make their speed zero. 
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chetangarg
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Re: Fox VS Duck Variation
« Reply #2 on: Jul 5th, 2007, 7:44pm » |
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on Jul 5th, 2007, 7:00pm, JiNbOtAk wrote:
Depends, is the fox trying to catch the rabbit, or the duck ? |
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No no no , actually there is no duck in this question. Only fox and rabbit, restricted to move in a circular area.
I think what ever be their initial position first of all fox will run towards the center and then from the center it will run towards the rabbit, as the rabbit changes the direction the fox changes too so that it heads directly towards the rabbit. and since they can't escape the circular area, so rabbit might be caught.
but i am not sure and infact i can't prove?
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JiNbOtAk
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Re: Fox VS Duck Variation
« Reply #3 on: Jul 5th, 2007, 8:27pm » |
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There are similar problems posted here. You can find the discussions here, here, here and here
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chetangarg
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Re: Fox VS Duck Variation
« Reply #4 on: Jul 5th, 2007, 8:44pm » |
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well JiNbOtak this is a different problem. before posting i had already read this threads.
in this question both can move inside the circle.
the rabbit is not restricted to move only on the circumference...
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Whiskey Tango Foxtrot
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Re: Fox VS Duck Variation
« Reply #5 on: Jul 5th, 2007, 9:46pm » |
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Then as long as the rabbit keeps moving he will not be caught.
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towr
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Re: Fox VS Duck Variation
« Reply #6 on: Jul 6th, 2007, 12:47am » |
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on Jul 5th, 2007, 9:46pm, Whiskey Tango Foxtrot wrote:| Then as long as the rabbit keeps moving he will not be caught. |
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At the very least the fox can get arbitrarily close, if I'm not mistaken.
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