Other Chessboard Problems

[!IMPORTANT] When a chessboard puzzle does not fit a familiar family, look for the hidden structure first: a row-column counting problem or a graph of legal moves.

Important properties

• In row-column problems, the placement can often be studied through the list of row totals and column totals before drawing any actual board picture.
• In custom-move puzzles, the right object is a graph whose vertices are squares and whose edges are allowed moves.
• “Visit every square and return to the start” is a Hamiltonian-cycle style question in that graph.
• The board picture is useful only after the counting or graph model is clear.

This topic groups together puzzles whose surface stories differ but whose solution method is the same: convert the board into a mathematical structure and reason there first.