Eight Queens Puzzle - Explicit Solutions

Explicit Solutions

Explicit solutions exist for placing n queens on an n × n board, requiring no combinatorial search whatsoever. The explicit solutions exhibit stair-stepped patterns, as in the following examples for n = 8, 9 and 10:

a b c d e f g h
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h
Explicit solution for 8 queens
a b c d e f g h i
9 9
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h i
Explicit solution for 9 queens
a b c d e f g h i j
10 10
9 9
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
a b c d e f g h i j
Explicit solution for 10 queens

Read more about this topic:  Eight Queens Puzzle

Famous quotes containing the words explicit and/or solutions:

    “Like dreaming, reading performs the prodigious task of carrying us off to other worlds. But reading is not dreaming because books, unlike dreams, are subject to our will: they envelop us in alternative realities only because we give them explicit permission to do so. Books are the dreams we would most like to have, and, like dreams, they have the power to change consciousness, turning sadness to laughter and anxious introspection to the relaxed contemplation of some other time and place.”
    —Victor Null, South African educator, psychologist. Lost in a Book: The Psychology of Reading for Pleasure, introduction, Yale University Press (1988)

    “Every man is in a state of conflict, owing to his attempt to reconcile himself and his relationship with life to his conception of harmony. This conflict makes his soul a battlefield, where the forces that wish this reconciliation fight those that do not and reject the alternative solutions they offer. Works of art are attempts to fight out this conflict in the imaginative world.”
    —Rebecca West (1892–1983)