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Wolf in a field (Posted on 2006-02-23) Difficulty: 3 of 5
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.

No Solution Yet Submitted by goFish    
Rating: 3.0000 (10 votes)

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Solution re: solution | Comment 14 of 17 |
(In reply to solution by Salil)

Salil is on the right track.  The dogs must be at least sqrt(2) times faster than the wolf in order to keep him penned pen. 

If they are sqrt(2) times faster, then having one each NE, NW. SE, and SW works. (See Leming's or my initial solution)

If they are not sqrt(2) times faster, then the wolf can lure 2 of them by going just up to the middle of the West edge of the square.  Now, he can exit by running directly to either the center of the North or the South edges, because the two on the the West edge can't catch him, and the other two can't both cover both exit points.

  Posted by Steve Herman on 2006-02-24 17:27:16

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