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In this problem we consider the movement of the knight in a game of chess. If you are unfamiliar with this, please see the reference

In this problem we consider the movement of the knight in a game of chess. If you are
unfamiliar with this, please see the reference material for this problem, Figure 10.6.5.
The knight we are considering is on the standard 88 chessboard. We use the standard
notation to references the spaces on this board.
For example, a knight located at d4 can move to any of the spaces, c2,e2,f3, b3, b5,
f5, c6, e6.
We may make a graph as follows. The vertices of this graph correspond to the 64
spaces on the chessboard. Two vertices are connected when ever a knight on one space
may move to the other space. For example we see that there is an edge between d4
and c2. Use this graph to answer the following questions.
(a) Can a knight that begins on b1, after a series of moves, end on c1? If so, what is
the minimum number of moves that this would take? Explain.
(b) For a knight that begins on b1 is there any space on the board that it cannot
occupy after any series of moves?
More generally, for any starting position is there any position to which a knight
cannot move to from there?
(c) Let the distance between two spaces x,y on the board (relative to a knight's
travel) be the minimum number of moves for a knight to move from x to y.
Starting at b1, which space(s) is/are the "farthest away" from here?
More generally, what is the largest distance between any two spaces on the chess-
board for a knight?
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