OFFSET
0,5
REFERENCES
Donald E. Knuth, Constraint Satisfaction (volume 4, fascicle 7a of The Art of Computer Programming, in preparation).
LINKS
Sam Loyd, A Crow Puzzle, in Brooklyn Daily Eagle, 20 December 1896, for the case n=8.
Mathematics Stack Exchange, Are there large n-queens solutions without 3-in-a-line? (2023).
Ho Boon Suan, The n queens problem with no three on a line, MathOverflow, Nov. 2023.
Wikipedia, No three in line problem.
Wikipedia, Eight Queens Puzzle, [Of the twelve fundamental solutions on the 8x8 chessboard, only "Solution 10" satisfies no three in a line. In "Solution 9" the queens on a5, e3 and g2 are in one line. - Vaclav Kotesovec, Nov 08 2023]
EXAMPLE
For n=8, place queens for rows 1..8 into columns 3,6,8,2,4,1,7,5, i.e.,
.
+-----------------+
| . . Q . . . . . |
| . . . . . Q . . |
| . . . . . . . Q |
| . Q . . . . . . |
| . . . Q . . . . |
| Q . . . . . . . |
| . . . . . . Q . |
| . . . . Q . . . |
+-----------------+
.
and rotate and/or reflect to get the other seven ways.
.
(Note that solutions such as
.
+-----------------+
| . . Q . . . . . |
| . . . . . Q . . |
| . . . Q . . . . |
| Q . . . . . . . |
| . . . . . . . Q |
| . . . . Q . . . |
| . . . . . . Q . |
| . Q . . . . . . |
+-----------------+
.
do not count as the queens on rows 4, 6, and 7 are in a straight line.)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Don Knuth, Nov 07 2023
EXTENSIONS
a(21) from Martin Ehrenstein, Nov 08 2023
a(22) from Martin Ehrenstein, Nov 09 2023
a(23) from Martin Ehrenstein, Nov 10 2023
a(24) from Martin Ehrenstein, Nov 16 2023
a(25) from Martin Ehrenstein, May 02 2024
STATUS
approved