A knight’s tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once. If the knight ends on a square that is one knight’s move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed, otherwise it is open (from Wikipedia). Find a (closed) knight tour!
An initial position of 8 Queens on a chessboard is given. Now move exactly three of the Queens to other cells so that there will be 11 cells on the board which are not under attack. To move the Queens, it is not necessary to use proper ’Queen moves’. You may take them up and place them anywhere. Is there only one solution? The initial positions are as follows (1 means “a Queen is placed there”, 0 “no Queen is placed) :
Implement a linear algorithm for finding a solution of the n-queens problem.
Place a maximal number of Queens on a chessboard in such a way that they are not attacking each other (see [2] and [1]).
How many queens are needed, and in what position, so that every unoccupied square of the chessboard could be attacked directly by a queen? (see [2] and [1]).
What is the largest number of Bishops that can be placed on the chessboard without any Bishop attacking another? (see [2] and [1]).
Place as few Bishops as possible on an ordinary chessboard so that every square of the board will be occupied or attacked (see [2] and [1]).
Place as few Knights as possible on a chessboard in such a way that each square is controlled by at least one Knight, including the squares on which there is a Knight (see [2] and [1]).