Wolf and 50 sheep

Originally posted by coquette
Otherwise, it's a non-puzzle. They move at the same speed and the wolf can never catch a sheep that is moving away at the same speed.

I think you're misunderstanding something: player B can only move one sheep per turn. If he could move them all, then it would be a non-puzzle. But I don't see any obvious solution to the problem as stated.

Originally posted by CZeke
I think you're misunderstanding something: player B can only move one sheep per turn. If he could move them all, then it would be a non-puzzle. But I don't see any obvious solution to the problem as stated.

well then, with an infinite plane and any configuration, i am stumped, for it seems that the sheep could be placed equaly distant (on a huge circular tangent) infinitely distant from the wolf (impossible) and the wolf would simply start out in any direction and simply be able to outrun the fleeing sheep. as the sheep take their turns always going from the radius of the wolf, they would, of course, be getting "herded" into a death trap configuration, to be caught and eaten just one day shy of infinity (for them) so to speak. just a guess.

Originally posted by CZeke
I think you're misunderstanding something: player B can only move one sheep per turn. If he could move them all, then it would be a non-puzzle. But I don't see any obvious solution to the problem as stated.

The sheep are in a line. Player B moves the sheep at the end and that sheep pushes all the other sheep.

I think it's only possible for the wolf to catch the sheep under special circumstances, such as:

1) The wolf starts within 1 metre of one of the sheep.
2) The wolf and the sheep all lie on a straight line, with the wolf on one end and the sheep on the other.
3) The wolf can end his move between 2 sheep, with both sheep being within 1 metre of the wolf.

etc...

I think with perfect play from both sides, the wolf will be S.O.L. almost every time. Remember, it may not always be the best move to move directly away from the wolf. Even though the sheep give up ground by moving in a direction other than straight away, they may be able to get themselves into a position where the wolf can't catch them by doing so (i.e. if the sheep lay on a straight line more than 50 metres from the wolf, they should each move out to the side on their first and/or second turn so the wolf can't position himself behind them or within 1 metres of two sheep between them).