<s>[INST] Equilibrium distribution of a Markov Chain Can anyone please tell me or help me with this question shown below?
A drunken chess grandmaster dials a long string of digits on a standard telephone keypad (laid out as shown below). It takes more than alcohol to make a grandmaster forget the rules of chess, so each digit he dials is a knight's move away from the previous one (e.g. 4 can be followed by 3, 9, or 0). The choices are made at random, independently of previous ones, with all available knight's moves being equally likely to be chosen for each digit. 
Find the equilibrium distribution of this Markov chain. (Hint: it helps to use the symmetry, e.g. 1 and 3 must have the same equilibrium probability.)
1 2 3
4 5 6
7 8 9
  0

I seem not to understand the question at all. Unlike finding other equilibrium distribution of a Markov Chain question where it is shown as a transition matrix with state space given, could anyone please help on trying to "read" and "identify" this question?
Your helps would be much appreciated.
 [/INST] Hint: the transition matrix looks like this (1 is the first entry and 0 is the last in each row/column). I have assumed that if the grand master presses $5$ first, we will randomly pick the next digit uniformly. 
$$\left[\begin{array}{cccccccccc}
0 & 0 & 0 & 0 & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0\\
0 & 0 & 0 & \frac{1}{2} & 0 & 0 & 0 & \frac{1}{2} & 0 & 0\\
0 & 0 & \frac{1}{3} & 0 & 0 & 0 & 0 & 0 & \frac{1}{3} & \frac{1}{3}\\
\frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10}\\
\frac{1}{3} & 0 & 0 & 0 & 0 & 0 & \frac{1}{3} & 0 & 0 & \frac{1}{3}\\
0 & \frac{1}{2} & 0 & 0 & 0 & \frac{1}{2} & 0 & 0 & 0 & 0\\
\frac{1}{2} & 0 & \frac{1}{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & 0 & 0 & 0
\end{array}\right]$$
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