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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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re: Okay, then prove this: | Comment 8 of 17 |
(In reply to Okay, then prove this: by Eric)

If the speed of the dogs. is only 1.4 times the wolf's then it's strategy could be go "Almost to any corner then trek around to the opposite corner staying the same "safe" distance from the edge. then when all four dogs are in the same corner run for the opposite corner and it is free..

Example using a 10'x10' square....total diagonal distance is 14.1421 feet. If the wolf approaches a corner and stays 1 foot from the edge it will have 3 dogs in that corner(assuming that the dogs only move if the "side the are currently protecting is threatened)  then staying 1 foot from the edge circles the field until it has all four dogs in one corner and is 1 foot from the corner on the diagonal. if it runs along the diagonal it needs to go more than 13.1421 feet to safety...the dogs however must travel 20'.  in the time the dog travels 13.1421 feet the dogs would have traveled only 18.399 feet giving the wolf 1.601 feet to get free.

Edited on February 23, 2006, 5:51 pm
  Posted by Wallace North on 2006-02-23 17:49:16

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