If-we-had-a-maze-which-was-contained-within-the-shape-of-a-square-and-it-has-one-enterence-on-its-edge-and-a-centre-point-from-which-you-start-If-you-move-randomly-you-will-naturally-escape-Now

Question Number 5150 by FilupSmith last updated on 21/Apr/16

If we had a maze, which was contained

within the shape of a square, and it has

one enterence on its edge, and a centre

point from which you start, If you move

randomly, you will naturally escape .

Now, lets say the maze itself is generated

at completely random odds .

You start in the middle, and each move you

make (left, right, up, down), is random .

If I place another person in this maze

at a random point, and they too move

at random, which is the more likely outcome :

a) Person 2 lands on the same position

as you do

b) You escape the maze

(T h i s q u e s t i o n I t h o u g h t o f o n m y o w n

a n d a m e x t r e m e l y c u r i o u s o n

e v e r y o n e s o p i n i o m o n t h i s)

Commented by prakash jain last updated on 23/Apr/16

Let us say you have n \times n grid .

To create a random maze you choose some

of the n^{2} line and put walls on those lines .

This means a number m is randomly chosen

between 1 to n^{2} . t h e n m walls are created

by randomly choosing m lines in n^{2} grid .

Calculating probability of the person

moving randomly will need be calculated

for each case m and then a conditional probability

will need to be summed .

more work to be done .

Commented by FilupSmith last updated on 24/Apr/16

That is very similar to my usumption .

Thanks!