|
I haven't put any information on how to compile, because if you don't know how to compile C code, then none of this makes much sense to you anyways. No explainations for how the source works are given other than the comments, which aren't bad. Source code for permute.c Source code for queens.c Source code for rotate.c Header file for rotate.h Sample permute.c output Complete graphic solutions |
|
FINAL 12 SOLUTIONS FOR 8 QUEENS PROBLEM Wed Jan 20 16:44:41 EST 1999 |
| The 8 queens problem is stated: Arrange 8 queens on a chess board such that no queen is under attack by another one. |
|
This solution was derived and verified using the following
steps:
Assume that at the very least, no queen can be in the same column or row of another queen. This means that each queen is on a unique row and column. Figure out all 40,320 ways the digits 1-8 can be arranged. This was done using the program permute.c. Peruse each 40,320 possible solutions in order and check if they work. ( Small work for a computer. ) This was done with the program queens.c. Finally, after finding 92 solutions, discover which ones are duplicates of others through reflection or rotation. This was done with a combination of inspection and the program rotate.c. This solution set eliminates any replications through the use of reflection and/or rotation. Including reflection and rotation there would be 92 solutions. Solution 10 is self-symmetrical and would only produce 3 additional solutions through reflection and rotation. It's also the easiest to memorize, if you ever want to win a bet. |
(1.) 04752613 (2.) 05726314 (3.) 13572064 Q . . . . . . . Q . . . . . . . . Q . . . . . . . . . . Q . . . . . . . . Q . . . . . Q . . . . . . . . . . . Q . . . . . . . Q . . . . . Q . . . . . . . Q . . . . Q . . . . . . . . . . . . Q . . Q . . . . . . . . . . . Q . . . Q . . . . . . . . . . . Q . . . . Q . . . . Q . . . . . . . . Q . . . . . . . Q . . . . . . . . . . . . Q . . . . Q . . . . . . . . Q . . . . . . . Q . . . ================ ================ ================ (4.) 14602753 (5.) 14630752 (6.) 15063724 . Q . . . . . . . Q . . . . . . . Q . . . . . . . . . . Q . . . . . . . Q . . . . . . . . Q . . . . . . . . Q . . . . . . . Q . Q . . . . . . . Q . . . . . . . . . . Q . . . . . . . . . . Q . . . Q . . . . . Q . . . . . . . . . . Q . . . . . . . . . . . Q . . . . . . . Q . . . . . . . Q . . . . . Q . . . . . . . Q . . . . Q . . . . . . . . Q . . . . . . Q . . . . . . . . . Q . . . ================ ================ ================ (7.) 15720364 (8.) 16257403 (9.) 16470352 . Q . . . . . . . Q . . . . . . . Q . . . . . . . . . . . Q . . . . . . . . Q . . . . . . . Q . . . . . . . . Q . . Q . . . . . . . . . Q . . . . . Q . . . . . . . . . . Q . . . . . . . . . Q Q . . . . . . . . . . . . . . Q Q . . . . . . . . . . Q . . . . . . . . Q . . . . . . Q . . . . . . . . . . Q . Q . . . . . . . . . . . . Q . . . . . . Q . . . . . . Q . . . . . . Q . . . . . ================ ================ ================ (10.) 24170635 (11.) 24730615 (12.) 25147063 . . Q . . . . . . . Q . . . . . . . Q . . . . . . . . . Q . . . . . . . Q . . . . . . . . Q . . . Q . . . . . . . . . . . . . Q . Q . . . . . . . . . . . . . Q . . . Q . . . . . . . . Q . . . Q . . . . . . . Q . . . . . . . . . . . . . . Q . . . . . . Q . . . . . . . Q . Q . . . . . . . . . . Q . . . . . Q . . . . . . . . . . . . Q . . . . . . Q . . . . . . . Q . . . . . Q . . . . ================ ================ ================ |