Posers and Puzzles

Posers and Puzzles

  1. Joined
    25 Aug '06
    Moves
    0
    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. USA
    Joined
    02 Mar '07
    Moves
    8808
    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. Pittsburgh, PA
    Joined
    03 May '07
    Moves
    1452
    18 May '07 17:29
    depends on B's actions. He might just make the sheeps run toward the wolf. otherwise - no
  4. Standard memberuzless
    The So Fist
    Voice of Reason
    Joined
    28 Mar '06
    Moves
    9908
    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. Subscribercoquette
    Already mated
    Omaha, Nebraska, USA
    Joined
    04 Jul '06
    Moves
    955712
    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. B is for bye bye
    Joined
    09 Apr '06
    Moves
    27526
    18 May '07 19:24
    Yes the wolf player could 'round the sheep up' and eat I think all but one of them.
  7. Subscribercoquette
    Already mated
    Omaha, Nebraska, USA
    Joined
    04 Jul '06
    Moves
    955712
    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. Joined
    06 Jul '06
    Moves
    1163
    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. Subscribercoquette
    Already mated
    Omaha, Nebraska, USA
    Joined
    04 Jul '06
    Moves
    955712
    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. Pittsburgh, PA
    Joined
    03 May '07
    Moves
    1452
    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. Standard memberark13
    Enola Straight
    mouse mouse mouse
    Joined
    16 Jan '05
    Moves
    12804
    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. Standard memberDeepThought
    Losing the Thread
    Cosmopolis
    Joined
    27 Oct '04
    Moves
    80277
    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. Subscribercoquette
    Already mated
    Omaha, Nebraska, USA
    Joined
    04 Jul '06
    Moves
    955712
    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. Standard memberDeepThought
    Losing the Thread
    Cosmopolis
    Joined
    27 Oct '04
    Moves
    80277
    20 May '07 09:25
    Originally posted by coquette
    your questions are very revealing. please go to another thread.
    What'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.
  15. Joined
    31 May '06
    Moves
    30743
    20 May '07 09:331 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?
    If the sheep are all infinitely far from the wolf and each other at the start then no.
    If they are all packed together with the wolf in the centre then yes.
Back to Top