The Knightrider Theory

IMPORTANT: ALL THIS IS UNDER THE ASSUMPTION ON AN INFINITE BOARD WITH NO OBSTACLES.

A rook can go to any square on the board from anywhere in 2 moves. Same as a queen. A dragon knight (Bishop + Wazir) can go to any squares in 3 moves. but what about a knightrider?

We all know how a knightrider moves from variants such as The Lake, and wait, nothing else? Oh, Storming The Castle? Whatever. It is a ranging type of knight, and it is known to be various people's favourite pieces because of how unpredictable it is. 

It is quite trivial that a knightrider can move to any square in 4 moves, because a knight has 4 different directions, 

Those 4 rays. A knight can go anywhere with infinite moves, unlike some pieces that are color-blind. The final destination does not change solely b changing the order of the moves, not their directions. Thus, we can deduce that a knightrider can go anywhere in 4 moves.

But, can we push this further? How about 3 moves? How about 2?

Well, a knightrider can go to any square IN 3 moves. 

You might ask, what is the purpose of this pic? As you can see, you can go to any square marked in the same colors in 2 moves or less, because of the same reasons of a rook. That means, if you get your knightrider as the same color as the destination, which is possible no matter what in 1 move as indicated by the arrow, if you approach in the other directions, it crosses over all 5 'polarities'. Thus, if we add 2 + 1, we can go to any square in a maximum of 3 moves. Sorry if the color scheme is comfusing.

How about 2? Well, you cannot because of this simple example.

You cannot use a knightrider to travel between those 2 knights in 2 moves. It is quite trivial, I do not want to setup a math equation for this. 

Thanks for this shower thought that I actually made it into a forum.

Nice deductions. Very interesting.

cool

The last board works like that for the same reason a knight does. For a knight to move to an adjacent square, you do this (Shown above)

A knight rider, because it moves the same as a knight (albeit further) takes the same amount of moves to get there, which amounts to 3

(Also, don’t mind the king, I’m on an iPad right now. It’s tough to do fen boards like that :D

Nice. Very interesting