Chess Knight Tours Visit Every Square Once
A knight on a chessboard moves in an L-shape, jumping two squares one way and one square sideways, so it always lands on a square of the opposite color. Mathematicians proved that a single knight can tour all 64 squares of an empty board and return to its starting square in a closed loop called a closed knight's tour. These tours rely on careful planning that turns the puzzle into a graph-theory problem where each square is a node and each possible move is an edge.
💡 Fun detail:
Some knight tours can be drawn so that the path forms a perfect star or other symmetric shapes, showing how a simple game piece can create beautiful geometric art.
Source: Mathematical Association of America