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The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century.
The eight queens puzzle is a special case of the more general n queens problem of placing n non-attacking queens on an n×n chessboard. Solutions exist for all natural numbers n with the exception of n = 2 and n = 3.
1. The problem. The 4-Queens Problem1 consists in placing four queens on a 4 x 4 chessboard so that no two queens can capture each other. That is, no two queens are allowed to be placed on the same row, the same column or the same diagonal.
Hill Climbing may NOT reach to a goal state for n-queens problem. by moving a queen within its column. The best moves are marked with value 12.
Question 8 Explanation: For an 8-queen problem, there are 92 possible combinations of optimal solutions.
Explanation: For a 10-queen problem, 724 possible combinations of optimal solutions are available.
Explanation: For 88 chess board with 8 queens there are total of 92 solutions for the puzzle.
To solve this problem, we will make use of the Backtracking algorithm. The backtracking algorithm, in general checks all possible configurations and test whether the required result is obtained or not. For thr given problem, we will explore all possible positions the queens can be relatively placed at.
Generally, it is 8. as (8 x 8 is the size of a normal chess board.) Output: The matrix that represents in which row and column the N Queens can be placed. If the solution does not exist, it will return false.