If there is at least one empty cell, every cell could be covered more than one way, and there is a way to cover all the cells, there is another way to cover all the cells?

Your reasoning is wrong. I give you example. Could you find more than one way for cover this cells?

110000
011000
001100
000000
000000
000000

this case works, only by making "one-way" steps i can fill the board,
11GGEE
211FFD
2311CD
4388CB
46699B
5577AA

note that "EVERY cell could be covered more than one way"
in your case this wrong for cell (2,1)

Edited by author 27.04.2008 02:03