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  • $\begingroup$ I'd appreciate it if this was on the bounty answer but I'll accept this I guess. $\endgroup$ Commented Oct 31, 2014 at 9:58
  • $\begingroup$ @warspyking I'll try to tie them together $\endgroup$ Commented Oct 31, 2014 at 10:01
  • $\begingroup$ What is the meaning of reachable? From what w are you talking about? There are a lot of quadruples (w1,w2,w3,w4) of distinct walks that cover all squares of a color. 3 examples are found in How many bishops to walk across the board. If s is a1 (using the board coordinates as used in the algebraic chess notation) what is w? $\endgroup$ Commented Nov 1, 2014 at 11:55
  • $\begingroup$ @miracle173 Hi. I have added a definition of "reachable" in the accepted version of this answer. $w$ is just any arbitrary walk - it doesn't matter what the walk was. I'm aware of that link - I linked to it - and had an answer on that question too $\endgroup$ Commented Nov 1, 2014 at 14:29