Magic tours are a rather unique variation of the magic square. On a magic
tour of order n the numbers of 1 to $$n^2$$ are layed out in such a way that
the knight piece (chess, moves in L shape) can move around consecutively
from 1 to $$n^2$$. There are magic and semimagic tours and if the full tour
can be closed, meaning that the knight can move from the $$n^2$$ location to
1, it will be deemed closed/re-entrant (otherwise it is called open).
Magic tours can never be created on magic squares with odd orders, but are
always a solution for squares of order
4n for n>2. All the solutions for the magic
tour of order 8 were unknown until August 5 2003 (by Guenter
Stertenbrink), after a computer went past every single solution. The
computer showed there were a total of 140 different semimagic tours and
the most magic tour was discovered by Francony in 1882. This magic tour
has the diagonals equal to 264 and 256, which is the closest a semimagic
tour of order 8 comes to a magic tour. A closed magic tour of order 16 was
created by Joseph Steen Madachy in 1979. Magic tours for other chess
pieces also exist, for example this one for king moves (picture right).
