Have you ever wondered how many moves it takes a Knight to get round the chess board, landing on every square?
Get out your chess board and try it. Place a Knight on any square and see how many moves it
takes you to cover the entire board. Make sure you don't miss any squares!
(Tip: use a coin, or button, to cover each square you visit so you know you don't have to go
there again.)
|
It is a hard puzzle because the Knight jumps over squares and you have to go backwards to make sure you don't miss any. You may also find that you need to go back to a square you have visited already, but the more times you visit a square the longer it will take you to get round the whole board! |
Is it possible to get across the board landing on each square only once?
Yes, starting from any square on the chess board the Knight can visit every other square in
just 63 moves! This is known as a Knight's Tour.
|
Click the board to see the Knight move from one side to the other in only 63 moves. |
If you don't believe the Knight covered every square, click again. This time we will cover up each square after the Knight visits it.
This Knight's Tour was discovered by William Beverley from London in 1848 and published in the Philosophical Magazine.
Is it possible for the Knight to get back to the square it started from?
Yes, but it takes one extra move (64 moves in all). This is a Closed Knight's Tour.
|
Click the board to see the Knight go round the board and return to its starting point in 64 moves. Again if you click a second time we will cover up each square after the Knight visits it. |
This symmetrical Closed Knight's Tour was published by Carl Wenzelides in the German Chess Periodical Schachzeitung in 1849, shortly after Beverley's Tour was first published. Carl was a retired archivist who lived in Nicolsburg, Hungary and spent the last years of his life working on chess problems and the complexities of Knight's Tours.
This time we are going to take Wenzelides' Tour and put a number on each square. The square
the Knight starts on will be 1, the second square will be 2, and so on.
|
|
|
|
|
Anatoly Karpov playing a simultaneous chess match against the winners of each age category at the FIDE World Youth Championships, Belfort, France, July 2005. Photo by Douglas MacGregor. |