KNIGHT’S TOUR

One of the oldest puzzles dating from the 14th century.  The problem is to find a sequence of 64 moves by which the knight can visit each square of the chessboard consecutively.  The possible solutions were never calculated. A “closed tour” is one in which the square at the end of a knight’s tour is a knight moved away from the first square, as in the second example below.  The master of Shatranj as-Suli published the following two closed tours:

The first example shows perfect axial symmetry on the left halfboard, the second is composed of two quasi-symmetrical half-board tours.