# Wolf and 50 sheep

David113
Posers and Puzzles 18 May '07 14:27
1. 18 May '07 14:271 edit
There are a wolf and 50 sheep on an infinite plane. Player A controls the wolf, and player B controls the sheep. Player A on his turn moves the wolf in any direction, but not more then 1 meter. Player B on his turn may move a single sheep, also in any direction but not more than 1 meter. Can the wolf catch a sheep for any initial configuration?
2. 18 May '07 17:09
Originally posted by David113
There are a wolf and 50 sheep on an infinite plane. Player A controls the wolf, and player B controls the sheep. Player A on his turn moves the wolf in any direction, but not more then 1 meter. Player B on his turn may move a single sheep, also in any direction but not more than 1 meter. Can the wolf catch a sheep for any initial configuration?
no they can't
3. 18 May '07 17:29
depends on B's actions. He might just make the sheeps run toward the wolf. otherwise - no
4. uzless
The So Fist
18 May '07 18:13
Originally posted by David113
There are a wolf and 50 sheep on an infinite plane. Player A controls the wolf, and player B controls the sheep. Player A on his turn moves the wolf in any direction, but not more then 1 meter. Player B on his turn may move a single sheep, also in any direction but not more than 1 meter. Can the wolf catch a sheep for any initial configuration?
seems the wolf could catch lots of sheep if they were standing next to each other to start with.

If the sheep were all lined up in a row standing next to each other, and player B moved one sheep at a time, then the wolf would eventually get them all.
5. coquette
18 May '07 19:15
yes, the wolf could catch one of the sheep.

the wolf dresses in "sheep's" clothing. the "sheep mover" would have no way of recognizing that one of the "sheep" was actually a wolf and would be taken in a surprize assault. After the attack, the sheep mover would need to simply keep track of which of the ones was actually a wolf.

if you have a problem with this answer, then you have never heard of a "wolf in sheep's clothing," or are assuming information not presented in the original premise, or you simply lack an imagination.

by the way, the only way the scenario works, is if (1) all the pieces move in one round, and (2) if this little exercise in deceit by costume is allowed. 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.
6. 18 May '07 19:24
Yes the wolf player could 'round the sheep up' and eat I think all but one of them.
7. coquette
18 May '07 20:11
Originally posted by Gastel
Yes the wolf player could 'round the sheep up' and eat I think all but one of them.
no, not if each sheep or wolf occupies one space, after the first attack, the sheep would all simply move one equal distance away from the wolf each move
8. 18 May '07 21:42
It really depends on the starting position,

if the sheep are in a circle with the wolf in the middle of the circle and with the sheep spaced 3 metres apart then the wolf would never catch any sheep.

however if the wolf stays at the door he can eat them all as they're getting of the plane when it lands
9. coquette
18 May '07 21:44
Originally posted by iraqi insurgent
It really depends on the starting position,

if the sheep are in a circle with the wolf in the middle of the circle and with the sheep spaced 3 metres apart then the wolf would never catch any sheep.

however if the wolf stays at the door he can eat them all as they're getting of the plane when it lands
oh yeah! that's right. silly me. of course.
10. 18 May '07 23:141 edit
Originally posted by iraqi insurgent
It really depends on the starting position,

if the sheep are in a circle with the wolf in the middle of the circle and with the sheep spaced 3 metres apart then the wolf would never catch any sheep.

however if the wolf stays at the door he can eat them all as they're getting of the plane when it lands
err... I have a suspicious idea that 'plane' here has a different meaning from what you infer:-)
11. ark13
Enola Straight
19 May '07 01:15
Originally posted by iraqi insurgent
It really depends on the starting position,

if the sheep are in a circle with the wolf in the middle of the circle and with the sheep spaced 3 metres apart then the wolf would never catch any sheep.

however if the wolf stays at the door he can eat them all as they're getting of the plane when it lands
Initially, I disagreed with you, but you're absolutely right. The circle clearly being the ideal starting position, as long as the sheep are sufficiently spaced, the wolf will be unable to catch them.

The way the wolf can catch a sheep is if he gets himself nearly colinear with two sheep and infinitely close to one of them. The closer sheep must run directly away from the wolf and straight into the other. How close to colinear do they have to be? Close enough that when a line is drawn between the wolf and his closer prey, the further sheep will be within 1 meter of that line.

Okay, so how does this fit in to the initial starting position? Well, the wolf starts running directly toward one sheep. (Running at the space between sheep wouldn't help as they are spaced far apart that the wolf could never have the potential to reach both in the same move.) For simplicity, let's say that the target sheep doesn't do anything until the wolf is infinitely close to it (this should be to the wolf's benefit, so it can be used to prove that the wolf can't catch any). At this point, the sheep moves directly away. Seeing that he will never catch this sheep by pursuing it in this manner, the wolf picks a new target. This time it's a little more complicated, but any target the wolf picks should be far enough away to position itself to be chased at such an angle that the path they take will not come within the aforementioned 1 meter limit of another sheep that would allow the wolf to catch a sheep. The more you space the sheep out to start with, the easier it is to observe this fact.
12. DeepThought
19 May '07 23:131 edit
Originally posted by David113
There are a wolf and 50 sheep on an infinite plane. Player A controls the wolf, and player B controls the sheep. Player A on his turn moves the wolf in any direction, but not more then 1 meter. Player B on his turn may move a single sheep, also in any direction but not more than 1 meter. Can the wolf catch a sheep for any initial configuration?
How close does the wolf have to be to the sheep in order to be considered to have caught it? Is less than 1 metre good enough? How close are the sheep allowed to come to oneanother - can I have two sheep with the same centre of mass position?
13. coquette
19 May '07 23:57
Originally posted by DeepThought
How close does the wolf have to be to the sheep in order to be considered to have caught it? Is less than 1 metre good enough? How close are the sheep allowed to come to oneanother - can I have two sheep with the same centre of mass position?
your questions are very revealing. please go to another thread.
14. DeepThought