a description of the logic to calculate 8-queens solutions recursively.

8-queens-recursive-logic.txt

ways to arrange 8 queens on an 8x8 board =
  ways to arrange 8 queens on an 8x8 board with queen at (7,0)
  ways to arrange 8 queens on an 8x8 board with queen at (7, 1)
  ways to ... with queen at (7, 2)
  ways to ... with queen at (7, 3)
  ways to ... with queen at (7, 4)
  ways to ... with queen at (7, 5)
  ways to ... with queen at (7, 6)
  ways to ... with queen at (7, 7)
  = 8 branches
  Each one of these "branches" can be computed by calculating:
    ways to ... with queen at (7, 2)  =
      ways to ... with queen at (7, 2)  and (6, 0)
      ways to ... with queen at (7, 2)  and (6, 4)
      ways to ... with queen at (7, 2)  and (6, 5)
      ways to ... with queen at (7, 2)  and (6, 6)
      ways to ... with queen at (7, 2)  and (6, 7)
      = 5 branches
      (We don't need to check the other 3 possibilities, because it would violate the
      solution constraints)
      etc...