There is a wolf in the centre of a square field, and four dogs in the corners. The wolf can easily kill one dog, but two dogs can kill the wolf. The wolf can run all over the field, and the dogs -- along the fence (border) only. Prove that if a dog's speed is 1.5 times more than the wolf's, then the dogs can prevent the wolf escaping.

This problem seems to be more complicated than I thought.

Let us say the wolf is at 0,0 & the four dogs at (0.5,0.5) (0.5,-0.5), (-0.5,-0.5) & (-0.5,0.5)

what happens if the wolf moves to (0.25,0.25) and then (0.125, 0.375) & moves back to (0.125,0.25)

2^0.5 should be the answer but this may generate answer closer to 1.5. don't know!

 

 

Posted by salil on 2006-02-26 04:16:59