Firstly a description of the pieces:
A
kNight is a (1,2) leaper which features in
Chess. It can move 1 cell horizontally + 2 cells vertically, or 1 cell vertically + 2 cells horizontally. A
kNight @ r5c5 can move to 8 cells: r37c46+r46c37.
A
Quad-kNight is a (4,8) leaper, i.e. move 4 times the distance as a
kNight. A
Quad-kNight @ r1c1 can move to 2 cells: r5c9+r9c5. There exists only one
Quad-kNight's circuit on a 9x9 board: r1c1-r5c9-r9c1-r1c5-r9c9-r5c1-r1c9-r9c5-r1c1.
With Non-Consecutiveness based on these 2 pieces here is a valid puzzle with one single given clue:
(Without any given clue there would be 8 solutions, all equivalent to each other via reflection/rotation.)
But the above puzzle is (probably) solvable only by computer programs using brute force, so here is a human-solvable version with 3 more given clues and the QNNC property replaced by the AC (Anti-Camel) property:
(A
Camel is a (1,3) leaper. It can move 1 cell horizontally + 3 cells vertically, or 1 cell vertically + 3 cells horizontally. A
Camel @ r5c5 can move to 8 cells: r28c46+r46c28.)