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).

from the said reference

I quote:
Semi-Magic Square Knight Tours
Without the aid of a computer, I've easily created many more Knight Tours and even a Semi-Magic Square Knight's Tour where all the rows and columns add up to the same number. In fact, every other vertical pair of numbers adds up to 49 and 81 respectively while the four major quadrants each add up to 520 and the four main sets of 2x2 squares in each quadrant add up to 130. The numbers 49 and 81 are significant since 49 is 7 squared in which 7 represents the shape of the Knight's move. Also, 81 is 9 squared in which 9 represents the first known Magic Square (3x3 square or 9 squares) from about 2200B.C.
........... etc

GO AHEAD AND READ IT- THE ALGORITHM IS HINTED...

ady

Posted by Ady TZIDON on 2004-04-13 11:46:55