4 ms·

Am I missing something? My reasoning is that the lion will easily catch the lion tamer by moving straight towards him/her. If the tamer moves in the same direct

by frooxie 15y ago

Am I missing something? My reasoning is that the lion will easily catch the lion tamer by moving straight towards him/her. If the tamer moves in the same direction, he/she will eventually hit a wall. If the tamer moves in any other direction, the lion will be able to move at least slightly closer to it. Repeat until caught. Or?

onemoreact 15y ago
It really just depends on how you model time and space. Assume that the lion and man are on a hex grid and the lion is 1 unit from the man. The man can now move to 3 spaces without being caught and change his orientation relative to the lion, which assuming the grid is reasonably large allows for him to move along a closed loop though space which means he can stay alive. If on the other hand the man is moving +/- 1 X and or Y on an XY grid at (1,0) and the lion is at (0,0) then the man must move to (2,Y) or risk being eaten which means his X must increase which mean he will eventually hit a wall. PS: If the lion can always get within striking distance of the man then there is no difference between moving at the same time and alternating, because the lion can chose randomly and then catch back up on a miss which enables him to win eventually.
- SonicSoul 15y ago
  what part of this question makes it a possibility that they're on a grid and can only move in 4 directions? in regular world (which is used to host this riddle) humans and animals can move diagonally as well.
  - onemoreact 15y ago
    Let's change the rules slightly. Take a ring one mile in diameter and assume the lion needs to get within 1 foot of the tamer. They both move at 1 inch per tick of game clock in any direction. To make things simple the the lion goes to the center of the ring, then aims for 2 inch closer to the ring than the tamer. Well the tamer will either go closer to the wall or the lion get's closer to him every second. But while he runs along the wall the lion takes a shorter path closer to the center of the ring, catches him and eats him. Also, if the tamer ever goes closer to the center of the ring in any turn the lion get's closer to him that turn because the lion stays on a line between the center of the ring and the tamer. The reason my example does not work for this puzzle is simply there is no distance closer the the center of the ring the lion can aim for and still get to eat him. At which point you need to think about what space looks like for points that are really close to each other.
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andylei 15y ago
from the article: > We split time into a sequence of intervals, of lengths t1, t2, t3, . . .. At the ith step the man runs for time ti in a straight line that is perpendicular to his radius vector at the start of the step. He chooses to run into the half plane that does not contain the lion (if the lion is on the radius then either direction will do). So certainly the lion does not catch the man in this time step. The man then repeats this procedure for the next time step, and so on.

by frooxie 15y ago

onemoreact 15y ago

It really just depends on how you model time and space. Assume that the lion and man are on a hex grid and the lion is 1 unit from the man. The man can now move to 3 spaces without being caught and change his orientation relative to the lion, which assuming the grid is reasonably large allows for him to move along a closed loop though space which means he can stay alive. If on the other hand the man is moving +/- 1 X and or Y on an XY grid at (1,0) and the lion is at (0,0) then the man must move to (2,Y) or risk being eaten which means his X must increase which mean he will eventually hit a wall. PS: If the lion can always get within striking distance of the man then there is no difference between moving at the same time and alternating, because the lion can chose randomly and then catch back up on a miss which enables him to win eventually.

SonicSoul 15y ago
what part of this question makes it a possibility that they're on a grid and can only move in 4 directions? in regular world (which is used to host this riddle) humans and animals can move diagonally as well.
- onemoreact 15y ago
  Let's change the rules slightly. Take a ring one mile in diameter and assume the lion needs to get within 1 foot of the tamer. They both move at 1 inch per tick of game clock in any direction. To make things simple the the lion goes to the center of the ring, then aims for 2 inch closer to the ring than the tamer. Well the tamer will either go closer to the wall or the lion get's closer to him every second. But while he runs along the wall the lion takes a shorter path closer to the center of the ring, catches him and eats him. Also, if the tamer ever goes closer to the center of the ring in any turn the lion get's closer to him that turn because the lion stays on a line between the center of the ring and the tamer. The reason my example does not work for this puzzle is simply there is no distance closer the the center of the ring the lion can aim for and still get to eat him. At which point you need to think about what space looks like for points that are really close to each other.

deleted 15y ago

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andylei 15y ago

from the article: > We split time into a sequence of intervals, of lengths t1, t2, t3, . . .. At the ith step the man runs for time ti in a straight line that is perpendicular to his radius vector at the start of the step. He chooses to run into the half plane that does not contain the lion (if the lion is on the radius then either direction will do). So certainly the lion does not catch the man in this time step. The man then repeats this procedure for the next time step, and so on.