ow many solutions are there for 8 queens on 8*8 board?ans.12919392 Previous Marked for Review Next

To find the number of solutions for the 8 queens problem on an 8x8 chessboard, we can approach it through combinatorial reasoning and backtracking algorithms. However, since this is a known problem, I will summarize the findings related to the number of configurations:

Explanation of the Problem

1. Problem Definition: The 8 queens puzzle involves placing 8 queens on a standard chessboard such that no two queens threaten each other. This means that no two queens can share the same row, column, or diagonal.

2. Known Results: The total number of distinct solutions for the 8 queens problem has been determined through systematic counting and algorithmic approaches. It is established that there are 92 unique solutions when considering the rotational and reflectional symmetries of the board.

3. Solution Enumeration: The problem can also be extended to consider solutions that do not consider symmetry (i.e., counting each rotation and reflection as distinct). In that case, the total becomes 12,672 configurations.

In summary, if you consider distinct arrangements (ignoring symmetries), the total number of solutions for the 8 queens on an 8x8 board is 92. If we were to include solutions from all symmetrical forms, it results in 12,672 configurations.

Final Answer

The unique solutions for the 8 queens problem on an 8x8 board is 92.