In chess, a knight can move in any direction, but it must move two spaces then turn and move one more space. The eight possible moves a knight can make from a given space are shown in the figure.

A knight's tour is a sequence of moves by a knight on a chessboard (of any size) such that the knight visits every square exactly once. If the knight's tour brings the knight back to its starting position on the board, it is called a closed knight's tour. Otherwise, it is called an open knight's tour. Determine if the Knight's tour shown in the figure is a Hamilton path, an Euler trail, or both, for the graph of all possible knight moves on an eight-by-eight chess board in which the vertices are spaces on the board and the edges indicate that the knight can move directly from one space to the other. Explain your reasoning.

Recall from the section Euler Circuits, as part of the Camp Woebegone Olympics, there is a canoeing race with a checkpoint on each of the 11 different streams as shown in the figure. The contestants must visit each checkpoint.