The diagram below represents a solution to the ____

Concept: The N-Queens problem asks for an arrangement of N queens on an N×N chessboard so that no two queens attack each other. Since a queen attacks along its entire row, column, and both diagonals, a valid placement must give every queen a distinct row, a distinct column, and a distinct diagonal from every other queen.

Application: For the given diagram (N = 8), the queens sit at row-column pairs (0,0), (1,6), (2,4), (3,7), (4,1), (5,3), (6,5) and (7,2). Every row number 0–7 and every column number 0–7 appears exactly once, so no two queens share a row or a column. Checking every pair of queens also confirms no two lie on a common diagonal (the absolute (magnitude) difference between their row numbers never equals the absolute difference between their column numbers). All three attack directions are therefore avoided.

Cross-check: This rules out the other named puzzles, each of which uses a different rule:

• Knight's Tour: a single knight must visit all 64 squares once via L-shaped moves - one moving piece, not eight simultaneously placed pieces.

• King's Problem: only forbids two kings from sitting on directly adjacent squares (including diagonal neighbours) - a much looser rule than requiring a distinct row, column, and diagonal for every piece.

• Rook's Problem: only forbids sharing a row or a column - it places no restriction on diagonals at all.

Since the arrangement satisfies the full row, column, and diagonal separation that only the Eight Queens condition requires, the diagram is a valid solution to the Eight Queens Problem.