Friday, August 24, 2018

[zxltoktj] Longer-range knight

Variations on creating a fairy chess piece inspired by the knight but more powerful:

A piece that can jump to any square reachable by 2 consecutive knight moves (sub-moves), both in the outward direction (distance from start point increases).  Unlike nightrider, the sub-moves do not have to be in the same direction.  The intermediate square does not have to be clear.  What does the target area look like as the number of sub-moves increases?

A piece that can jump to any square reachable by a rook move plus a bishop move, in either order.  Both sub-moves have to be in the outward direction.  The intervening squares do not have to be clear.  In 2D, this piece is probably way too powerful, able to jump to almost any empty square on the board, roughly the complement of the queen.  In 3D and higher dimensions, it isn't quite so all powerful.  We could also decrease the power of rooks and bishops in higher dimensions or require intervening squares be clear to decrease power.

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