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 Non-Attacking Chess Pieces II (Posted on 2010-08-23)
Arrange all sixteen white pieces and the black king on a standard 8x8 chessboard such that no piece is in check by another piece. The arrangement must be possible to reach following rules of standard play (though such play would be ludicrous), with no pawn having reached the eighth row for promotion.

 See The Solution Submitted by Dej Mar No Rating

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 a computer solution | Comment 3 of 7 |

DECLARE SUB place (ptr!)
CLEAR , , 25000
DIM SHARED bd(8, 8), attacked(8, 8), pcs\$, rook1row, b1par, prevp

pcs\$ = "qrrbbnnkpppppppp"

CLS
place 1
END

SUB place (ptr)
FOR r0 = 1 TO 8
SELECT CASE r0
CASE 1
row = 8
CASE 2
row = 7
CASE 3
row = 6
CASE 4
row = 5
CASE 5
row = 4
CASE 6
row = 3
CASE 7
row = 2
CASE 8
row = 1
END SELECT
FOR col = 1 TO 8
IF attacked(row, col) = 0 AND bd(row, col) = 0 THEN
p\$ = MID\$(pcs\$, ptr, 1)
good = 1
SELECT CASE p\$
CASE "q"
FOR r = 1 TO 8
c = col - (row - r)
IF c > 0 AND c < 9 THEN IF bd(r, c) > 0 THEN good = 0: EXIT FOR
c = col + (row - r)
IF c > 0 AND c < 9 THEN IF bd(r, c) > 0 THEN good = 0: EXIT FOR
IF bd(r, col) > 0 THEN good = 0: EXIT FOR
IF bd(row, r) > 0 THEN good = 0: EXIT FOR
NEXT r
IF good THEN
FOR r = 1 TO 8
c = col - (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) + 1
c = col + (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) + 1
attacked(r, col) = attacked(r, col) + 1
attacked(row, r) = attacked(row, r) + 1
NEXT r
bd(row, col) = ptr
place ptr + 1
bd(row, col) = 0
FOR r = 1 TO 8
c = col - (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) - 1
c = col + (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) - 1
attacked(r, col) = attacked(r, col) - 1
attacked(row, r) = attacked(row, r) - 1
NEXT r
END IF
CASE "r"
IF row > rook1row THEN
FOR r = 1 TO 8
IF bd(r, col) > 0 THEN good = 0: EXIT FOR
IF bd(row, r) > 0 THEN good = 0: EXIT FOR
NEXT r
IF good THEN
FOR r = 1 TO 8
attacked(r, col) = attacked(r, col) + 1
attacked(row, r) = attacked(row, r) + 1
NEXT r
bd(row, col) = ptr
rook1row = rook1row + row
place ptr + 1
rook1row = rook1row - row
bd(row, col) = 0
FOR r = 1 TO 8
attacked(r, col) = attacked(r, col) - 1
attacked(row, r) = attacked(row, r) - 1
NEXT r
END IF
END IF
CASE "b"
IF b1par > 0 AND (b1par + row + col) MOD 2 = 0 THEN good = 0
IF good THEN
FOR r = 1 TO 8
c = col - (row - r)
IF c > 0 AND c < 9 THEN IF bd(r, c) > 0 THEN good = 0: EXIT FOR
c = col + (row - r)
IF c > 0 AND c < 9 THEN IF bd(r, c) > 0 THEN good = 0: EXIT FOR
NEXT r
IF good THEN
FOR r = 1 TO 8
c = col - (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) + 1
c = col + (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) + 1
NEXT r
bd(row, col) = ptr
b1par = b1par + row + col
place ptr + 1
b1par = b1par - row - col
bd(row, col) = 0
FOR r = 1 TO 8
c = col - (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) - 1
c = col + (row - r)
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) - 1
NEXT r
END IF
END IF
CASE "n"
FOR r = row - 2 TO row + 2
IF r > 0 AND r < 9 AND r <> row THEN
cdiff = 3 - ABS(row - r)
FOR c = col - cdiff TO col + cdiff STEP 2 * cdiff
IF c > 0 AND c < 9 THEN IF bd(r, c) > 0 THEN good = 0: EXIT FOR
NEXT
END IF
IF good = 0 THEN EXIT FOR
NEXT
IF good THEN
FOR r = row - 2 TO row + 2
IF r > 0 AND r < 9 AND r <> row THEN
cdiff = 3 - ABS(row - r)
FOR c = col - cdiff TO col + cdiff STEP 2 * cdiff
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) + 1
NEXT
END IF
NEXT
bd(row, col) = ptr
place ptr + 1
bd(row, col) = 0
FOR r = row - 2 TO row + 2
IF r > 0 AND r < 9 AND r <> row THEN
cdiff = 3 - ABS(row - r)
FOR c = col - cdiff TO col + cdiff STEP 2 * cdiff
IF c > 0 AND c < 9 THEN attacked(r, c) = attacked(r, c) - 1
NEXT
END IF
NEXT
END IF
CASE "k"
FOR r = row - 1 TO row + 1
IF r > 0 AND r < 9 THEN
FOR c = col - 1 TO col + 1
IF c > 0 AND c < 9 THEN
IF bd(r, c) > 0 THEN good = 0: EXIT FOR
END IF
NEXT
IF good = 0 THEN EXIT FOR
END IF
NEXT
IF good THEN
FOR r = row - 1 TO row + 1
IF r > 0 AND r < 9 THEN
FOR c = col - 1 TO col + 1
IF c > 0 AND c < 9 THEN
IF r <> row OR c <> col THEN attacked(r, c) = attacked(r, c) + 1
END IF
NEXT
END IF
NEXT

bd(row, col) = ptr
place ptr + 1
bd(row, col) = 0

FOR r = row - 1 TO row + 1
IF r > 0 AND r < 9 THEN
FOR c = col - 1 TO col + 1
IF c > 0 AND c < 9 THEN
IF r <> row OR c <> col THEN attacked(r, c) = attacked(r, c) - 1
END IF
NEXT
END IF
NEXT
END IF
CASE "p"
IF prevp > 0 THEN IF row * 8 + col < prevp THEN good = 0
IF good THEN
IF row > 1 AND row < 8 THEN
IF col - 1 > 0 THEN IF bd(row - 1, col - 1) > 0 THEN good = 0
IF col + 1 < 9 THEN IF bd(row - 1, col + 1) > 0 THEN good = 0
IF good THEN
IF col - 1 > 0 THEN attacked(row - 1, col - 1) = attacked(row - 1, col - 1) + 1
IF col + 1 < 9 THEN attacked(row - 1, col + 1) = attacked(row - 1, col + 1) + 1

bd(row, col) = ptr
IF ptr < 16 THEN
place ptr + 1
ELSE
good = 0
FOR r = 1 TO 8
FOR c = 1 TO 8
IF bd(r, c) = 0 THEN
IF attacked(r, c) = 0 THEN
good = 1
FOR rchk = r - 1 TO r + 1
FOR cchk = c - 1 TO c + 1
IF rchk > 0 AND rchk < 9 AND cchk > 0 AND cchk < 9 THEN
IF bd(rchk, cchk) > 0 THEN good = 0: EXIT FOR
END IF
NEXT: IF good = 0 THEN EXIT FOR
NEXT
END IF
END IF
IF good THEN EXIT FOR
NEXT: IF good THEN EXIT FOR
NEXT
IF good THEN
prevpSave = prevp
prevp = 8 * row + col
PRINT
FOR r = 1 TO 8
FOR c = 1 TO 8
IF bd(r, c) = 0 THEN
IF attacked(r, c) = 0 THEN
PRINT "* ";
ELSE
PRINT ". ";
END IF
ELSE
PRINT MID\$(pcs\$, bd(r, c), 1); " ";
END IF
NEXT: PRINT
NEXT
prevp = prevpSave
END IF
END IF
bd(row, col) = 0

IF col - 1 > 0 THEN attacked(row - 1, col - 1) = attacked(row - 1, col - 1) - 1
IF col + 1 < 9 THEN attacked(row - 1, col + 1) = attacked(row - 1, col + 1) - 1
END IF
END IF
END IF
END SELECT
END IF
NEXT
NEXT
END SUB

finds:

`. n . * . . k .. p . . . . . .. n . p p . p b. b . . . . . .. p . . p . p p. . . . . r . .. . r . . . . .q . . . . . . .`

where the * refers to the black king. The letters refer to the white pieces.

Other solutions may exist, but the program was stopped here.

In fact, cycling the rightmost file to become the leftmost results in another solution:

` . . n . * . . k . . p . . . . . b . n . p p . p . . b . . . . . p . p . . p . p . . . . . . r . . . . r . . . . . q . . . . . .`

but this can't be continued as then one of the bishops would be attacking the white king.  And it can't be done with ranks as then either a pawn would be in promotion position or the queen would be attacking a knight.

Of course either solution could be reflected.

 Posted by Charlie on 2010-08-23 21:01:20

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