# Looking into the Knights Tour

• 12 months ago · Quote · #1

Somewhere in the 17th Century or so, a mathemetician named Euler created an 8x8 magic square than had the interesting feature that if a Knight was placed on a8 (1) and followed the numerics to 64 (h6), the next move, if a second board was set up, would place the Knight back on a8 (1 again).

In the years to come, we would regard this as the Knights Tour. This exercise, while really having no real application in over the board play (especially with the 50 Move Rule that FIDE devised), still challenges players in the fact that the sequence needed to be memorized is part of a very difficult pattern to remember.

However, there are many ways to look at the Tour and at least 16 to 32 (and possibly more) ways to accomplish.

One of the easiest ways is to break the board into sectors of 4x4 squares and to limit the shapes to at most 2 different    designs. Typically, the 2 most basic shapes to create with the Knight could be classified into "Diamonds" and "Squares".

A diamond shape would consist of say, placing a Knight on a8 and moving to say, b6-d5-c7, while the square shape would entail moving a knight on say, a7 to c8-d6-b5.

In the illustration below the following conditions will reign:

1.) Black will move the King around the board but never capture the Knight if possible (otherwise there is no Tour to take).

2.) On move 15, Black will move his pawn (but again not capture) in order to avoid the 50 move rule.

KEYS TO THE TOUR

Our Sectors are (in order of areas the knight enters):

Queenside (a5-d5-a8-d8): 1

Queenside (a1-d1-a5-d5): 2

Kingside (e1-h1-e4-h4): 3

Kingside (e5-h5-e8-a8): 4

Our shape patterns are:

Diamond Shapes (a8-c7-d5-b6)

Square Shapes (a7-c8-d6-b5)

Here then is the Knight's Tour simplified:

Continued Tomorrow (sorry for the delay, folks).

• 11 months ago · Quote · #2
• 11 months ago · Quote · #3

Thank you

• 11 months ago · Quote · #4

Interesting....

what does the diamond look like?

• 11 months ago · Quote · #5
VULPES_VULPES wrote:

Interesting....

what does the diamond look like?

I just updated the posting. The Diamond pattern is any pattern such as moving from a8 to c7 to d5 to b6. This is the pattern that will allow you toreach the corners of the board.

• 11 months ago · Quote · #6

I apologize. Apparently, unless I am either super fast (or lucky), the site has a hard time posting my threads. Hopefully I can get it to work here shortly.