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Fischer Random Chess. Play from a random setup. (8x8, Cells: 64) (Recognized!)[All Comments] [Add Comment or Rating]
Tony Quintanilla wrote on Thu, Nov 11, 2004 01:39 AM EST:
The following e-mail was received by the editors: 

Great website! You write:
 

	'Fischer Random Chess has 960 legal arrays. This number is determined as
follows: 

	First, place the two Bishops. There are 16 different ways for one bishop
to be on a white square and the other Bishop to be on a black square. 

	That leaves six empty squares. Now, place the King somewhere between the
two Rooks. There are 20 different ways for a King and two Rooks to occupy
six squares with the King in between. 

	That leaves three squares for the two Knights and the Queen. There are
three possible ways to place these pieces. 

	Thus, there are 16 x 20 x 3 (960) legal arrays in Fischer Random
Chess.'

	 

	The most complex step is that 20 in the middle. It can be removed like
this:

		Fischer Random Chess has 960 legal arrays. This number is determined as
follows: 

		First, place the two Bishops. There are 16 (4 x 4) different ways for
one bishop to be on a white square and the other Bishop to be on a black
square. 

		That leaves six empty squares. Now, place the Queen. There are 6
different ways to do this. 

		That leaves five empty squares. Now, place the two Knights. There are 10
different ways to do this. 

		That leaves three empty squares. Lastly, place the two Rooks and the
King. There is only one legal way to do this. 

		Thus, there are 16 x 6 x 10 x 1 (960) legal arrays in Fischer Random
Chess. 

		Regards 

		Peter Ridges