A Magic Tour is a tour where, if you number each square with the corresponding knight's step, the result *is* a magic square.

A Semi-Magic Tour is a tour where, if you number each square with the corresponding knight's step, the result *is* a semimagic square.

(A magic square, as you may already know, is one in which the respective sums of the numbers in all the rows, columns, and long diagonals, add up to the same number -- whereas -- a semimagic square is one in which the respective sums of the numbers in all the rows, columns, but not necessarily the diagonals, add up to the same number.)
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The problem:
Find a Magic Tour, on a standard 8x8 chessboard, or prove that it is impossible.

If you find that is is impossible, find a Semimagic Tour, on a standard 8x8 chessboard or prove that it is impossible. Show your work!

So, the first square the knight is on, is marked (1). The next square the knight jumps to is marked (2), and so on... until (64).

* For extra credit, make sure that, at the end, the knight is exactly one knight's move away from the starting square.
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Since "Knight's Tour" is a term used outside the scope of this problem, I'm sure you can find an answer on the internet. Please find an independent solution.

This may require a computer program (hence the category).

Also read Gamer's post Explanations.

Those scary numbers only pertain if SilverKnight were asking for ALL magic tours. But his puzzle reads "Find a Magic Tour". Just one. That is probably over my head, but someone like Charlie is quite capable of coming up with an intelligent algorithm to solve this. 

Edited on April 13, 2004, 8:00 am

Edited on April 13, 2004, 8:01 am

Posted by Penny on 2004-04-13 07:55:05