All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Algorithms
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Fear filled dogs strategy | Comment 13 of 17 |
I can't find a killer-wolf strategy that beats the fearfilled-dogs strategy.
These fearfilled dogs run to each other, so that there are two groups, one couple of dogs guards two sides, the other couple controls the other two sides.  There is a diagonal that connects the corners where the two groups meet.  If the wolf is on one side of the diagonal, the couple that is responsible for those sides is in control, they go to the point where a line perpendicular to the diagonal and running through the wolf, cuts the side line.  The other group of wolves goes to the point that is found by drawing a line that goes through the group in control and the wolf.
When the wolf passes the diagonal, "control" is taken by the other group.  When the wolf is on the diagonal, every group acts as if it is not in control.
The highest speed needed is 1.41 wolf speed.
  Posted by Hugo on 2006-02-24 10:31:50
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information