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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
The knight we are considering is on the standard chessboard. We use the standard
notation to references the spaces on this board.
For example, a knight located at can move to any of the spaces, b b
f c e
We may make a graph as follows. The vertices of this graph correspond to the
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
and Use this graph to answer the following questions.
a Can a knight that begins on b after a series of moves, end on c If so what is
the minimum number of moves that this would take? Explain.
b For a knight that begins on b 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 on the board relative to a knight's
travel be the minimum number of moves for a knight to move from to
Starting at b which spaces isare 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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