12-Feb-1995
Unsolved Problem 7:
Is there a magic knight's tour on an 8 X 8 chessboard?
A knight's tour of a chessboard is a sequence of
moves by a knight such that each square of the board
is visited exactly once.
If the successive squares are numbered from 1 to 64,
in order, the tour is called a magic tour if
the resulting square is a magic square.
A magic square is a square array of numbers
such that each row and column and the two main diagonals
sum to the same number (the magic constant).
Semi-magic knight's tours are known (in which the rows
and columns sum to the same number, but the diagonals
do not sum to that number).
Reference:
- [Dudeney 1970]
- H. E. Dudeney,
Amusements in Mathematics.
Dover. New York: 1970.
Page 127, problem 412.
Magic Knight's Tour
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