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Attack! (Posted on 2004-01-17)

Place 1 king, 2 queens, and 5 knights on a standard 8ﾗ8 chessboard so that every unoccupied square is under attack.

Submitted by DJ

Rating: 4.5556 (9 votes)

Solution: (Hide)

One Knight: ｷｷｷｷｷｷｷｷｷｷ x ｷ x ｷｷｷｷ x ｷｷｷ x ｷｷｷｷｷ n ｷｷｷｷｷ x ｷｷｷ x ｷｷｷｷ x ｷ x ｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷ Two Knights: ｷｷｷｷｷｷｷｷｷｷ x x x x ｷｷｷ x x ｷｷ x x ｷｷｷｷ n n ｷｷｷｷ x x ｷｷ x x ｷｷｷ x x x x ｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷｷ Three Knights: ｷｷｷｷｷｷｷｷｷｷ x x x x ｷｷｷ x x ｷ x x x ｷｷ x ｷ n n x ｷｷｷ x x n ｷ x x ｷｷ x x x x x ｷｷｷｷ x ｷ x ｷｷｷｷｷｷｷｷｷｷｷ Four Knights: ｷｷｷｷｷｷｷｷｷｷ x x x x ｷｷｷ x x x x x x ｷｷ x x n n x x ｷｷ x x n n x x ｷｷ x x x x x x ｷｷｷ x x x x ｷｷｷｷｷｷｷｷｷｷ Four Knights, One Queen: Q x x x x x x x x x x x x x ｷｷ x x x x x x x ｷ x x x n n x x ｷ x x x n n x x ｷ x x x x x x x ｷ x ｷ x x x x ｷｷ x ｷｷｷｷｷｷｷ Four Knights, Two Queens: Q x x x x x x x x x x x x x ｷ x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x x ｷ x x x x x x x x x x x x x Q
That leaves two pieces (a King and a Knight) to place, and only two spaces on the board not occupied or under attack.
You can take care of one of those spots with the King, and the other with the Knight.
Barring reflections, the King can be placed in six different ways:
Q x x x x x x x x x x x x x ｷ x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x x K x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x ｷ x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x K x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x ｷ x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x x x x x x x x x K x x x x x x Q Q x x x x x x x x x x x x x ｷ x x x x x x x x x x x x n n x x x x x x n n x x x K x x x x x x x x x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x ｷ x x x x x x x x x x x x n n x x x x x x n n x x x x K x x x x x x x x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x ｷ x x x x x x x x x x x x n n x x x x x x n n x x x x x K x x x x x x x x x x x x x x x x x x x x Q
The Knight can be place in one of two spots, again barring reflections:
Q x x x x x x x x x x x x x n x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x x ｷ x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x x x x x x x x ｷ x x x x x x x x x x x x x Q
However, three of the King placements and one of the Knight placements can be reflected, leaving more unique possibilities for the combination:
Q x x x x x x x x x x x x x n x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x x K x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x n x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x K x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x n x x x x x x x x x x x x n n x x x x x x n n x x x x x x x x x x x x x x x x x x x K x x x x x x Q Q x x x x x x x x x x x x x n x x x x x x x x x x x x n n x x x x x x n n x x x K x x x x x x x x x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x n x x x x x x x x x x x x n n x x x x x x n n x x x x K x x x x x x x x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x n x x x x x x x x x x x x n n x x x x x x n n x x x x x K x x x x x x x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x x x x x x x x K x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x x x x x x x K x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x x x x x x x x x x x x x x x x K x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x x x x x x x x x x x x x x x K x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x K x x x x x x x x x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x x x x x x x x x x x x x x x x x K x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x K x x x x x x x x x x x x x x x x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x x x x x x x x x K x x x x x x x x x x x x Q Q x x x x x x x x x x x x x x x x x x x n x x x x x x n n x x x x x x n n x x x x x K x x x x x x x x x x x x x x x x x x x x Q
That's 15 arrangements in all. Each one can be reflected horizontally, vertically, and both (making 60 total), and all but three can be reflected through the SW-NE axis, making a grand total of 72 unique arrangements.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-01-30 02:20:02
my solution	Michael	2004-08-22 10:03:30
re(2): Another solution	Sing4TheDay	2004-04-27 15:47:53
re: Another solution	Billy Bob	2004-04-25 13:14:36
Another solution	Sing4TheDay	2004-04-22 16:59:52
I agree with Tristan	Billy Bob	2004-04-21 17:35:31
re: One solution	Lisa	2004-04-21 13:08:05
impossible....	chuck	2004-02-07 12:38:46
re: One solution	SilverKnight	2004-01-21 12:02:29
One solution	Tristan	2004-01-17 16:38:40

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