eightqueens

Eight Queens refers to a classic chess puzzle that asks whether eight queens can be placed on an 8x8 chessboard so that no two attack each other. Since a queen attacks along rows, columns, and diagonals, a valid arrangement must have exactly one queen in each row and each column, with no two sharing a diagonal.

The puzzle has a well-known result: there are 92 distinct solutions when every arrangement is counted as separate, and 12 unique solutions when solutions that can be transformed into each other by rotations or reflections are considered the same. Solutions can be represented compactly as a permutation of the numbers 1 through 8, where the i-th entry indicates the column in which the queen sits in the i-th row.

Solving the eight queens puzzle is a common example in computer science and combinatorics, often approached with backtracking or constraint propagation. A typical method places one queen per row, then recursively attempts valid placements in subsequent rows, pruning positions that would create diagonal conflicts. This problem also serves as a gateway to the broader N-Queens problem, which asks for placing N queens on an N×N board. The number of solutions varies with N, and the puzzle illustrates concepts such as recursion, search trees, and symmetry reduction.

Variants and generalizations extend beyond eight and the standard board size, exploring larger boards, fewer or more queens, and additional rules. The eight queens problem remains a staple in puzzle communities and programming education for its clarity and computational elegance.