Research on Knight′s Circuit Problem in Generalized Chessboards and Their Solutions
Ning Xuan-xi · Nanjing Hangkong Hangtian Daxue xuebao · 2004
The knight′s circuit problem is an attractive research point for a long time and a completely unsolved hard nut. Especially, the problem of whether there is a knight′s circuit in a generalized chessboard of m×n, m≠n , is less studied. For example, there has been no published result about the solution to the knight′s circuit in a 9×10 Chinese chessboard. In this paper the solutions to the 9×10 Chinese chessboard and to the 5×6,6×6,7×6,5×8,6×8,7×8,5×10,6×10,7×10,8×10,9×10,9×8,9×6 generalized chessboards, which are defined as root chessboards, are given. The method for constructing a knight′s circuit in a larger chessboard from these 13 root chessboards is also presented. It is proved that there are knight′s circuits in the chessboards m×n, when m≥5,n≥5 and the product of m and n is an even number.