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Knight's Tour (3 & 4) (Posted on 2004-04-12) Difficulty: 5 of 5
Please see Knight's Tour (2) for the rules of a Knight's Tour.

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).

No Solution Yet Submitted by SilverKnight    
Rating: 3.0000 (4 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solution (With Great Assistance from Others)Gordon Steel2004-04-13 15:32:47
Hints/Tipsre: a good referenceAdy TZIDON2004-04-13 11:46:55
Hints/Tipsa good referenceAdy TZIDON2004-04-13 11:39:24
Hints/Tipsre: ExplanationsSilverKnight2004-04-13 11:13:51
e.g., please read "My comment was very dumb". You are not being fair to SKPenny2004-04-13 07:55:05
re: I'll have the answer in about an hour or so....e.g.2004-04-13 07:51:42
My comment was very dumb.Penny2004-04-12 20:01:30
ExplanationsGamer2004-04-12 18:18:14
I'll have the answer in about an hour or so....Penny2004-04-12 18:10:36
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