The Knight's Tour
An Extremely Simple Solution
I would like to share a Knight's Tour I created by using a
very simple rule I devised that requires no memorization:
Start at any corner and continuously rotate in the same direction
around the board moving on the outermost squares.
The moves create a semi-symmetrical pattern around the board. The tour is
completed with only four trips around the board. Feel free to post this
solution on your web-pages, other publications, or with other Knight Tour
enthusiasts. Please reference my name and e-mail address when posting my
design and Knight's Tour solution.
The simple Knight's Tour shown above was included in Manus Patrick Fealy's book: The Great Pawn Hunter Chess Tutorial on page 237.
I originally created the chess board in Excel which I could also use to automatically
sum the rows, columns, and diagonals. My Knight's Tour does not reflect a
Magic Square but does provide an extremely simple solution. I recreated the
board in Visio and added the red lines to show the
symmetry. Connecting the sequential moves is fun to do with other Knight
Tours, Magic Squares, and Magic Cubes to come up with different designs.
In addition to being fun, the Knight's Tour puzzle also helps chess students
to develop their ability to visualize tricky knight move sequences. The Greater
Knoxville Chess Club's director wrote: "Thanks for the brainwork! I just started
using the knight's tour as an instructional device two weeks ago with my
students. Lev Alburt gives a solution in Comprehensive Chess Course starting
with a knight on d3. Your solution with the knight starting from a corner is
what I told my students that I would develop a methodology for. Now I don't
have to do nothing but present your work! Thanks for the assist -- you must have
read my mind!"
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Knight's Tour Solution
The Knight's Move Puzzle
If you enjoy puzzles like the one above, try the "Knight's Move" puzzle:
Starting with two black and two red knights positioned as in the box labelled "0" below, and using only
knight's moves, show how to exchange the positions of the black and red knights in seven moves.
The trick to this puzzle is knowing that the term 'move' does not constrain the knight to one jump,
elsewise there would actually be 16 separate moves. This puzzle was created in 1512 by Guarini
and normally labeled as "The Puzzle No Mortal Can Solve." If you look at the actual number
of jumps by each knight, they go in the following sequence: 1 - 2 - 3 - 4 - 3 - 2 - 1 (16 jumps,
7 moves). If you take the square-root of 1234321, you end up with 1111. I'll let your
imagination figure out various ways to use the Knight's Move in math (octal/binary) and cryptography.
If you connect the lines for the odd moves (1, 3, 5, 7) or the even moves (2, 4, 6) only, they both make
a complete 8 pointed star.
www.BordersChess.org/KTsimple.htm modified 2007.04.15