Place 4 Kings, 4 Rooks, 2 Knights, and 1 Bishop on a conventional (8x8) chessboard in order that every square, whether occupied or vacant, is under attack.

How about placing 6 Kings, 2 Rooks, 2 Knights, and 1 Bishop on the said board, satisfying the same conditions?

 Part II:  I was able to do this with 6 Kings, 2 Rooks, and 1 Bishop.

_ _ _ _ _ _ _ _

_ K _ _ _ _ K _

_ _ K _ _ B _ _

_ _ _ R _ _ _ _

_ _ _ _ R _ _ _

_ _ _ _ _ K _ _

_ K _ _ _ _ K _

_ _ _ _ _ _ _ _

  The Rooks attack the centerlines, the Kings attack the corners, each other, and the Rooks. Meanwhile the Bishop keeps the Kings honest.

  If the 2 kNights have to be used, place them each in a corner.

Edited for clarity.

Edited on March 19, 2006, 7:11 pm

Posted by Leming on 2006-03-19 15:57:56