Show that there is no knight's tour on a 4 × 4 chessboard.
A knight is a chess piece that can move either two spaces horizontally and one space vertically or one space horizontally and two spaces vertically. That is, a knight on square (x, y) can move to any of the eight squares (x ± 2, y ± 1), (x ± 1, y ± 2), if these squares are on the chessboard, as illustrated Here

A knight's tour is a sequence of legal moves by a knight starting at some square and visiting each square exactly once. A knight's tour is called reentrant if there is a legal move that takes the knight from the last square of the tour back to where the tour began. We can model knight's tours using the graph that has a vertex for each square on the board, with an edge connecting two vertices if a knight can legally move between the squares represented by these vertices.