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.

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