A knight positioned in the corner of the board can make two moves while a knight positioned on a central square can visit eight possible squares. (Side question: Given a number between 2 and 8, is it possible for a knight to have that number of possible moves? For example a knight on b1 can make 3 possible moves.) In the previous post we examined problems in which a pawn could make the maximum possible number of moves. In this post we will examine problems in which a knight can make its maximum eight moves. Such problems are often known as task problems. When a black knight makes its eight possible moves and the theme is called a knight wheel. When a white knight makes its eight possible moves it is called a knight tour. As usual you will scroll down for the solution to my problems and click on the diagrams for the solutions to the other problems.

Here is my knight tour. The key is strong in the sense that it makes multiple threats but each of the threats are enforced. It is clear that the wSc4 will make the tour. See if you can spot the black defenses that force 2.Sf5 and 2.Se2. Scroll down for the solution.

Mansfield's classic knight wheel. If you read my last post you will recognized that this is a changed waiter. There is a mate set for every move of the bS but one of the mates must be changed. Brain Harley referred to this problem as a knight wheel with 9 spokes. 
No post on the knight wheels would be complete with out Heathcote's masterpiece. In the knight wheel task the threat will often be to capture the knight making the wheel. When the knight moves it defeats the threat. Here that is not the case. Here the key is 1.Rc7 threatening 2.Sc3. The move of bSd4 defeats the threat because it will open a flight square after the wS closes the wBb2's line. What follows is beautiful: 2 self blocks, 5 line interferences, and a self pin. 
We end our knight wheels with a beautiful little try problem. A wQ vs bS duel. The wQ can mate if it can just get access to a square in the bK's field. The wS can mate on b6 if a guard is placed on e5. Let's give it a shot. A clever device handles the cooktries, that try to capture the knight: 1.g3/g4/Qe1/Qh4 is met by 1...d3! which closes the line of guard to e4. So the wQ starts her march: 1.Qg1? (2.Qd4) Sf2! 1.Qf1? (2.Qc4) Sd6! 1.Qd1? (2.Qxd4) Sd2! 1.Qc1? (2.Qc4/Qc6) Sc3! 1.Qh2? (2.Sb6) Sg3! 1.Qh3? (2.Qe6) Sc5! 1.Qh5? (2.Sb6) Sg5! 1.Qh6? (2.Qe6/Qc6) Sf6! The only square left is 1.Qh8! with the double threat of 2.Qa8/Sb6. Wow. 
A now a monumental task problem. The double knight wheel (16 forced mates between two wS's) has been done by by Petrovic 1963. The matrix to the right does not quite accomplish because it only attains 15 distinct mates (2.Sg7 is missing). But it has a much better key and play. 
For the first problem the key 1.Re4 makes 7 threats (2.Sb3/Sc2/Sc6/Se6/Sf5/Sf3/Se2). The key gives a flight and the king's move 1...Kc5 forces 2.Sf5. The move 1...c2 forces 2.Se2. Moreover, 1...Sxb5 defeats all of the threats but finishes the knight tour. Answer to the side question: A knight can have 2,3,4,6, or 8 moves.