Chapter 6, Problem 6.26E

(Eight Queens) Another puzzler for chess buffs is the Eight Queens problem. Simply stated: Is it possible to place eight queens on an empty chessboard so that no queen is “attacking” any other—that is, so that no two queens are in the same row, the same column, or along the same diagonal? Use the kind of thinking developed in Exercise 6.24 to formulate a heuristic for solving the Eight Queens problem. Run your program. [Hint: It’s possible to assign a numeric value to each square of the chessboard indicating how many squares of an empty chessboard are “eliminated” once a queen is placed in that square. For example, each of the four corners would be assigned the value 22, as in Fig. 6.27.]

Once these “elimination numbers” are placed in all 64 squares, an appropriate heuristic might be: Place the next queen in the square with the smallest elimination number. Why is this strategy intuitively appealing?