I basically know whether the following statements are true, but I would like to know how they are proved.
- A knight kept anywhere on an empty chess board can not reach its adjacent square in exactly 8 moves.
- It is possible to fill the entire board with black and white knights such that no knight can kill another knight of the other colour.
- A knight that reaches a square in $n$ moves can not reach it in $n+1$ moves but can reach it in $n+2$ moves in atleast $n$ ways.
P.S. I'm not sure if my tags are ok.