Hello,

While learning about Markov Chain I came across the below problem:

**A simple Markov chain – cat and mouse**

Suppose there is a row of five adjacent boxes, with a cat in the first box and a mouse

in the fifth box. At each ‘tick’ the cat and the mouse both jump to a random box next

to them. On the first tick the cat must jump to box 2 and the mouse to box 4 but on

the next ticks they may jump to the box they started in or to box 3.

When the cat and mouse are in the same box the cat catches the mouse and the

Markov chain terminates. Because there is an odd number of boxes between the

cat and mouse it’s easy to see that they will not jump past each other.

So Markov chain that corresponds to this contains the only five possible

combinations of (Cat,Mouse).

```
State 1: (1,3) State 2: (1,5) State 3: (2,4) State 4: (3,5) State 5:
(2,2), (3,3) & (4,4) # => cat catches the mouse
The matrix P = [0 0 .5 0 .5; 0 0 1 0 0; .25 .25 0, .25 .25; 0 0 .5
0 .5; 0 0 0 0 1] represents the probabilities of the transition from one state to
the next and the question is how long has the mouse got before it's caught. Its best
chance is starting in State 2 = (1,5).
```

The matrix P is a stochastic matrix where all the probabilities along any row add up

to 1.

Can someone please help me in understanding the indented part??