18 May 07
1 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?
18 May 07
Originally posted by David113no they can't
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?
18 May 07
Originally posted by David113seems the wolf could catch lots of sheep if they were standing next to each other to start with.
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?
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.
18 May 07
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.
18 May 07
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
18 May 07
Originally posted by iraqi insurgentoh yeah! that's right. silly me. of course.
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
18 May 07
1 edit
Originally posted by iraqi insurgenterr... I have a suspicious idea that 'plane' here has a different meaning from what you infer:-)
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
19 May 07
Originally posted by iraqi insurgentInitially, 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.
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
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.
19 May 07
1 edit
Originally posted by David113How 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?
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?
19 May 07
Originally posted by DeepThoughtyour questions are very revealing. please go to another thread.
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?
20 May 07
Originally posted by coquetteWhat's been said above seems to assume pointlike wolves and sheep. The wolf can be up to 2 metres long from nose to tail, and sheep are about a metre long. Also they've assumed that the wolf always runs towards the nearest sheep, which isn't going to work. What the wolf could do in the circle configuration is run at a sheep to reposition itself so that it is outside the circle, and then try to herd them a bit so that when it attacks seriously the sheep get in each other's way. If the sheep are pointlike or they can move through one another then the wolf isn't going to catch any, if on the other hand they can't run through each other it is going to have a much easier time of it. Sadly for the wolf the plane described is infinite so you can position the sheep sufficiently far from each other that the fact that they are extended objects no longer matters.
your questions are very revealing. please go to another thread.
20 May 07
1 edit
Originally posted by David113If the sheep are all infinitely far from the wolf and each other at the start then no.
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?
If they are all packed together with the wolf in the centre then yes.