IBM Ponder This #044 · December 2001

Consider chess board of dimension 4 by N.

In a "closed knight's tour", we start at some square of the board, proceed by valid knight's moves, visit each square exactly once, and return to our starting point as the 4N+1st square.

An "open knight's tour" is similar, except that we stop at the 4Nth square, having visited all squares exactly once, and with no requirement that we ever return to the starting square.

Part 1:
For what N is there a closed knight's tour of the 4xN chessboard?

Part 2:
For what N is there an open knight's tour of the 4xN chessboard?

Solution

Best opened after a real attempt

To be added.