# The Knights Tour

“None shall pass.

What?

None shall pass.

I have no quarrel with you good sir knight, but I must cross this bridge.

Then you shall die.

I command you, as Arthur King of the Britians to stand aside.

I move... for no man.

So be it!”

The Dark Knight, Monty Python and the Holy Grail

Knight:

1.     A warrior, especially of the Middle Ages.

2.     A chess piece, often in the shape of a horse's head, that is moved two squares in one direction and one at right angles to that direction in a single move, leaping over any intervening pieces.

Chess Board:

1.       64 squares (eight rows and eight columns) arranged in two alternating colors (light and dark).

You can run but you cannot hide! It is you against the notorious Dark Knight. Where is the safest place to be while pursued by this ruthless warrior? We will investigate the trail of the knight on the chess board as it attempts to find you. Are these paths Open or Closed? Are they Intersecting or Non Intersecting? What is a Hamiltonian Path? We will investigate Warnsdorff's rule for trying to find you. Your role is to develop strategies and analyse the effectiveness of these strategies.  We will discuss the applications of these to our everyday lives and what does all this have to do with the 4th Dimensional Hypercube? We will conclude by using all this new knowledge to try and solve an 1870’s Cryptotour. Simple!

This spatial puzzle involves taking a chess piece (the Knight) for a 'walk' on a chess board and landing on every square exactly once. With its origins in the game of Chess,this puzzle is most engaging at many year levels. It has a compelling appeal that encourages students to 'stick at it'. While obviously a spatial puzzle, it is the class statistics that helps place the learning focus firmly on problem solving and strategy development. The various options of the companion software add significant power to the search.

See Maths300 The Knights Tour for activity description.

(Note Needs subscription: http://www.maths300.esa.edu.au/index.php?option=com_content&view=article&id=214)

Fourth Dimensional Hypercube moves:

d8,  b7,  a5,  b3,  d2,  f3, g5,  f7,  d6,  c4,  e5,  c6, d4,  e6,  c5,  e4,  g5,  e6, d8,  f7,  e5,  f3,  d4,  b3, c5,  b7,  d6,  e4,  d2,  c4, a5,  c6,  d8.

1870s Cryptotour