Originally posted by iamatigerI agree, if the ninja is not omnipotent, this could work probabilistically. It leaves only one of the corridors unchecked.
They can certainly make it very difficult for him by all running to one point, running out on different paths to the corners of a triangle, then all running clockwise or all anticlockwise (randomly. Then running back to the start point again and repeating. He has to keep on guessing correctly which way they will run.
Or to give him 1/3rd chance each tim ...[text shortened]... n out to the corners of a triangle, then two guards run to a random stationary guard and repeat.
Originally posted by forkedknightIt is as if it is all laid out in advance.This puzzle is thus a sort of maze, depending on the tetrahedron to define the six allowable turns of the paths. Each possible maze is entirely known to the ninja as he plans his route.
I agree, if the ninja is not omnipotent, this could work probabilistically. It leaves only one of the corridors unchecked.
However, the OP specifies that the ninja can anticipate all of the guards' moves, which means this strategy cannot work.
Originally posted by iamatigerI've been getting nowhere.
After much thought, I think he can always escape. The guards can pin him down to one of three paths, but they can only get it so that those three paths are in a triangle, (with them at each corner) and therefore can only check two of them at once; the ninja is in the unchecked path and escapes.
If the guards could pin the ninja down to three paths that ...[text shortened]... at a single point then they could get him, but that seems to be impossible as far as I can tell.
Originally posted by talzamir4 guards and it's game over, but I really don't see how it's solvable with 3.
In this puzzle, being a ninja simply means that the guards can't see her. No throwing stars, kuzari-gama, or wall-climbing.. and the slight speed difference simply means that if the ninja goes along some closed path and a guard chases her, say A-B-C-A-.. forever, the guard will eventually catch her.
Originally posted by forkedknightWhy would the speed advantage need to be more extreme? He only limits the amount of time you have to finite. I would think that if the guards knew that the ninja could predict their layout then they could catch him with an advantage in speed because they could then predict the ninja and minimize the time it takes them to change their strategy continually limiting the ninja untill they had him in a small enough area in a corridor where they covered all possible exits.
I'm trying to think how the guards could use their speed advantage to assist them. With a "slight" speed advantage, I don't really see how that helps, but was if the speed advantage was more extreme?