The N-Queens problem, with a different approach

Rebol N-Queens

REBOL [
    Title:  "n-queens"
    Author: "Gregg Irwin"
    Comment: {
        I just cooked this up in my head. It could fail miserably in some cases.
        The special N // 6 = 2 case isn't something I discovered, but the
        "pathing" algorithm used is mine.
    }
]


n-queens: func [
    "Returns a string describing the solution for the N Queens problem for N."
    n [integer!] "The size of the board on which to place the queens"
][
    if n < 4 [return "Sorry, there is no solution."]

    if all [even? n  2 <> remainder n 6] [ return rejoin [ {
        1) Start at R1C2, make knights moves (right 2 down 1) until you can't
           make any more moves without going off the board.
        2) Start at R} (n) "C" (n - 1) { , make knights moves (left 2 up 1) until you can't
           make any more moves without going off the board. This is a mirror
           image operation of step 1.
           }
        ]
    ]

    if all [even? n  2 = remainder n 6] [ return rejoin [ {
        1) Start at R1C} (n / 2) {, make knights moves (right 2 down 1) until you can't
           make any more moves without going off the board. Now, you're going
           to wrap back around to the left side of the board, dropping down to
           the next row from where you left off. You'll start in column }
           either even? n / 2 [2][1] {.
           You can also look at is as just continuing the knights move, but
           wrapping around the edge of the board.
           Keep going until you've placed } (n / 2) { queens total.
        2) Like before, do a mirror image operation of step 1, starting from
           R} (n) {C} (n / 2 + 1) { and working your way up and to the left.
           }
        ]
    ]

    if all [odd? n  2 <> remainder (n - 1) 6] [ return rejoin [ {
        1) Start at R1C2, make knights moves (right 2 down 1) until you can't
           make any more moves without going off the board.
        2) Start at R} (n) {C} (n) {, make knights moves (left 2 up 1) until you can't
           make any more moves without going off the board. This is a mirror
           image operation of step 1, but starting in the lower right corner.
           }
        ]
    ]

    if all [odd? n  2 = remainder (n - 1) 6] [ return rejoin [ {
        1) Start at R1C2, make knights moves (right 2 down 1) until you can't
           make any more moves without going off the board.
        2) Start at R} (n - 1) {C} (n) {, make knights moves (left 2 up 1) until you get
           to column 1. Place the queen for column 1 at R} (n) {C1. This is a mirror
           image operation of step 1, but starting one cell up from the lower
           right corner, and with a final "break move".
           }
        ]
    ]
]

print "solution for 3:"
print n-queens 3
print "solution for 5:"
print n-queens 5
print "solution for 6:"
print n-queens 6
print "solution for 8:"
print n-queens 8
print "solution for 14:"
print n-queens 14
print "solution for 9:"
print n-queens 9

halt