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h86m 14 ( +1 | -1 )
8 queens on a chessboard This is a nice little question.

How will you arrange 8 queens on an empty chessboard, so that no queen attacks any other queen?
invincible1 14 ( +1 | -1 )
hint A hint for all trying to slove this one. It will help to think on the lines of trying to place queens knight hops away..
mateintwo 6 ( +1 | -1 )
Queens placed in : a6,b3,c7,d2,e4,f8,g1,h5
seems to be a correct solution for me ,)

take care

Luca
invincible1 3 ( +1 | -1 )
Mestrinho There are plenty of solutions!!
olympio 3 ( +1 | -1 )
invincible you mean mateintwo? hehe
chessnovice 5 ( +1 | -1 )
... Exactly 60 solutions, in case you wanted to know.
invincible1 2 ( +1 | -1 )
Yes I meant mateintwo! :-)
pebbles 33 ( +1 | -1 )
Number of solutions There are 12 distinct solutions, not counting rotations and reflections.

11 of these give rise to 8 solutions each, when rotations and reflection of the board are considered to give different solutions.

The 12th gives rise to only 4 solutions by rotation, since it mirrors into itself.

Thus in total there are 92 solutions.
olympio 7 ( +1 | -1 )
pebbles are you sure that a few of the rotations and reflections of the 11 may overlap giving 60 instead?
buddie 14 ( +1 | -1 )
Interesting sideline: Maximum no. of Queens which don't attack each other is 8.
max no. of Rooks = 8.
Kings = 16.
Bishops = 14.
Knights = 32!
I'm not sure about pawns, but I would say 24.
pebbles 8 ( +1 | -1 )
olympio Below is a list of the 92 different solutions:

1 1 5 8 6 3 7 2 4
2 1 6 8 3 7 4 2 5
3 1 7 4 6 8 2 5 3
4 1 7 5 8 2 4 6 3
5 2 4 6 8 3 1 7 5
6 2 5 7 1 3 8 6 4
7 2 5 7 4 1 8 6 3
8 2 6 1 7 4 8 3 5
9 2 6 8 3 1 4 7 5
10 2 7 3 6 8 5 1 4
11 2 7 5 8 1 4 6 3
12 2 8 6 1 3 5 7 4
13 3 1 7 5 8 2 4 6
14 3 5 2 8 1 7 4 6
15 3 5 2 8 6 4 7 1
16 3 5 7 1 4 2 8 6
17 3 5 8 4 1 7 2 6
18 3 6 2 5 8 1 7 4
19 3 6 2 7 1 4 8 5
20 3 6 2 7 5 1 8 4
21 3 6 4 1 8 5 7 2
22 3 6 4 2 8 5 7 1
23 3 6 8 1 4 7 5 2
24 3 6 8 1 5 7 2 4
25 3 6 8 2 4 1 7 5
26 3 7 2 8 5 1 4 6
27 3 7 2 8 6 4 1 5
28 3 8 4 7 1 6 2 5
29 4 1 5 8 2 7 3 6
30 4 1 5 8 6 3 7 2
31 4 2 5 8 6 1 3 7
32 4 2 7 3 6 8 1 5
33 4 2 7 3 6 8 5 1
34 4 2 7 5 1 8 6 3
35 4 2 8 5 7 1 3 6
36 4 2 8 6 1 3 5 7
37 4 6 1 5 2 8 3 7
38 4 6 8 2 7 1 3 5
39 4 6 8 3 1 7 5 2
40 4 7 1 8 5 2 6 3
41 4 7 3 8 2 5 1 6
42 4 7 5 2 6 1 3 8
43 4 7 5 3 1 6 8 2
44 4 8 1 3 6 2 7 5
45 4 8 1 5 7 2 6 3
46 4 8 5 3 1 7 2 6
47 5 1 4 6 8 2 7 3
48 5 1 8 4 2 7 3 6
49 5 1 8 6 3 7 2 4
50 5 2 4 6 8 3 1 7
51 5 2 4 7 3 8 6 1
52 5 2 6 1 7 4 8 3
53 5 2 8 1 4 7 3 6
54 5 3 1 6 8 2 4 7
55 5 3 1 7 2 8 6 4
56 5 3 8 4 7 1 6 2
57 5 7 1 3 8 6 4 2
58 5 7 1 4 2 8 6 3
59 5 7 2 4 8 1 3 6
60 5 7 2 6 3 1 4 8
61 5 7 2 6 3 1 8 4
62 5 7 4 1 3 8 6 2
63 5 8 4 1 3 6 2 7
64 5 8 4 1 7 2 6 3
65 6 1 5 2 8 3 7 4
66 6 2 7 1 3 5 8 4
67 6 2 7 1 4 8 5 3
68 6 3 1 7 5 8 2 4
69 6 3 1 8 4 2 7 5
70 6 3 1 8 5 2 4 7
71 6 3 5 7 1 4 2 8
72 6 3 5 8 1 4 2 7
73 6 3 7 2 4 8 1 5
74 6 3 7 2 8 5 1 4
75 6 3 7 4 1 8 2 5
76 6 4 1 5 8 2 7 3
77 6 4 2 8 5 7 1 3
78 6 4 7 1 3 5 2 8
79 6 4 7 1 8 2 5 3
80 6 8 2 4 1 7 5 3
81 7 1 3 8 6 4 2 5
82 7 2 4 1 8 5 3 6
83 7 2 6 3 1 4 8 5
84 7 3 1 6 8 5 2 4
85 7 3 8 2 5 1 6 4
86 7 4 2 5 8 1 3 6
87 7 4 2 8 6 1 3 5
88 7 5 3 1 6 8 2 4
89 8 2 4 1 7 5 3 6
90 8 2 5 3 1 7 4 6
91 8 3 1 6 2 5 7 4
92 8 4 1 3 6 2 7 5

For instance, solution #1 reads as follows:
a1 b5 c8 d6 e3 f7 g2 h4
tonlesu 4 ( +1 | -1 )
pebbles You're not by any chance related to Arthur Fuerstein are you?
pebbles 3 ( +1 | -1 )
tonlesu: Nope, not at all, and not to Bobby F. either :))
tonlesu 5 ( +1 | -1 )
Yeah Bobby and Arthur used to pal around together.
chessnovice 8 ( +1 | -1 )
... Good call, pebbles. One of my solutions turned out wrong, so it ruined my data.
pebbles 100 ( +1 | -1 )
My output ... was generated by a little BASIC program I wrote. Here it is (it certainly can be improved upon):


OPEN "queens" FOR OUTPUT AS #1
counter = 0

FOR a = 1 TO 8

FOR b = 1 TO 8
IF a = b THEN GOTO 500
IF ABS(a - b) = 1 THEN GOTO 500

FOR c = 1 TO 8
IF a = c THEN GOTO 490
IF ABS(a - c) = 2 THEN GOTO 490
IF b = c THEN GOTO 490
IF ABS(b - c) = 1 THEN GOTO 490

FOR d = 1 TO 8
IF (d = a) OR (d = b) OR (d = c) THEN GOTO 480
IF ABS(d - a) = 3 THEN GOTO 480
IF ABS(d - b) = 2 THEN GOTO 480
IF ABS(d - c) = 1 THEN GOTO 480

FOR e = 1 TO 8
IF (e = a) OR (e = b) OR (e = c) OR (e = d) THEN GOTO 470
IF ABS(e - a) = 4 THEN GOTO 470
IF ABS(e - b) = 3 THEN GOTO 470
IF ABS(e - c) = 2 THEN GOTO 470
IF ABS(e - d) = 1 THEN GOTO 470

FOR f = 1 TO 8
IF (f = a) OR (f = b) OR (f = c) OR (f = d) OR (f = e) THEN GOTO 460
IF ABS(f - a) = 5 THEN GOTO 460
IF ABS(f - b) = 4 THEN GOTO 460
IF ABS(f - c) = 3 THEN GOTO 460
IF ABS(f - d) = 2 THEN GOTO 460
IF ABS(f - e) = 1 THEN GOTO 460

FOR g = 1 TO 8
IF (g = a) OR (g = b) OR (g = c) OR (g = d) OR (g = e) OR (g = f) THEN GOTO 450
IF ABS(g - a) = 6 THEN GOTO 450
IF ABS(g - b) = 5 THEN GOTO 450
IF ABS(g - c) = 4 THEN GOTO 450
IF ABS(g - d) = 3 THEN GOTO 450
IF ABS(g - e) = 2 THEN GOTO 450
IF ABS(g - f) = 1 THEN GOTO 450

FOR h = 1 TO 8
IF (h = a) OR (h = b) OR (h = c) OR (h = d) OR (h = e) OR (h = f) THEN GOTO 440
IF h = g THEN GOTO 440
IF ABS(h - a) = 7 THEN GOTO 440
IF ABS(h - b) = 6 THEN GOTO 440
IF ABS(h - c) = 5 THEN GOTO 440
IF ABS(h - d) = 4 THEN GOTO 440
IF ABS(h - e) = 3 THEN GOTO 440
IF ABS(h - f) = 2 THEN GOTO 440
IF ABS(h - g) = 1 THEN GOTO 440


counter = counter + 1
PRINT #1, counter, a; b; c; d; e; f; g; h


440 NEXT h
450 NEXT g
460 NEXT f
470 NEXT e
480 NEXT d
490 NEXT c
500 NEXT b
NEXT a

CLOSE
pebbles 59 ( +1 | -1 )
Correction In an earlier post I wrote:

"The 12th gives rise to only 4 solutions by rotation, since it mirrors into itself."

This should have been:

"The 12th gives rise to only 4 solutions: 2 by rotation and 2 by reflection." Indeed, rotating the board by 90 degrees gives a new solution, but turning it around by 180 degrees does not yield a new solution. See solution #14 in my list above.

I made this unforgivable gaffe by writing from memory, without checking; this puzzle is very old and has been known to me for a long time. So please don't be too harsh and have mercy on me.
pebbles 14 ( +1 | -1 )
I was almost correct this time "The 12th gives rise to only 4 solutions: the original (basic) solution, 1 new solution by rotation and 2 new solutions by reflection."

Clear at last.