Wolfram Schubert's N-Queens page

Here are a few results of the n-queens puzzle (esp variations of the "original" n-queens puzzle) split into subtasks.

The subtask results are published here to enable a probabilistic aproach of verifying the total solution numbers, i.e. without (re)performing the whole computations.

Number of (180deg) symmetric solutions to non-attacking queens problem on n X n board. See OEIS sequence A032522. OEIS b-file.

N	total solutions	subtask results
1	1
...	...
32	181254386312
33	533869114600	split into subtasks by 1 preset column
34	2419751731604	split into subtasks by 2 preset columns
35	6905549827664	split into subtasks by 2 preset columns
36	33686204023352	split into subtasks by 2 preset columns
37	97762487422768	split into subtasks by 4 preset columns

Notes: The values of columns preset0, preset1, ... are zero based.
"Preset0" is the first column from the middle of the board, "preset1" is the next column from the middle of the board.

Number of ways of placing n nonattacking superqueens (amazons) on an n X n board. See OEIS sequences A051223 and A051224.

N	total solutions A051223	subtask results	symmetric solutions (180°) (no known OEIS sequence)	symmetric solutions (90°) (no known OEIS sequence)	symmetric solutions count only once A051224 = (A051223 + 180degSymmSol + 2 * 90degSymmSol)/8
1	1		1	1	1
...	...		...	...	...
23	306819842212	split into subtasks by 3 preset columns	417684	0	38352532487
24	2883202816808	split into subtasks by 4 preset columns	1220024	920	360400504834
25	28144109776812	split into subtasks by 5 preset columns	3904588	908	3518014210402

Note: The values of columns preset0, preset1, ... are zero based.

Please send questions, notes, hints, error corrections, flames a.s.o. to email account "wschubnq" at the mail domain "gmx.de".

Last change: 01/18/2010