never mind about the cannons and missiles

if knights are generalized to be allowed to move to any piece a pythagorean distance 2 < D < sqrt(8) from their origination instead of a combination of rectilinear moves, it makes sense to let cannons do the same thing with 3 < D < sqrt(15) and missiles would get 4 < D < sqrt(24).

It would also make sense to do away with cannons and missiles entirely, as knights would have been effectively transformed in a way that allows use of all dimensions, and the whole introduction of offsides rules and possible extrapolations (such as, a king may demote itself to a pawn, that would be the king's move for the turn, coupled with a stricter offsides rule -- the spotter rule -- that only allows cannons or missiles to move to a position on a rank containing at least one pawn or piece that has been promoted from a pawn or let a pawn sit on the final rank unpromoted so it can function as a spotter) needed to allow additional pieces can be abandoned as a curious spike to file away in the unexpected event that c4d becomes dull and boring.

So. Never mind about the cannons and missiles and offsides or spotter rules, the second rank is all pawns (for now at least) and a knight at (3,3,3,3) can move to any of the 208 spaces at (1,2,2,2) (1,2,2,3) (1,2,2,4) (1,2,3,2) (1,2,3,3) (1,2,3,4) (1,2,4,2) (1,2,4,3) (1,2,4,4) (1,3,2,2) (1,3,2,3) (1,3,2,4) (1,3,3,2) (1,3,3,4) (1,3,4,2) (1,3,4,3) (1,3,4,4) (1,4,2,2) (1,4,2,3) (1,4,2,4) (1,4,3,2) (1,4,3,3) (1,4,3,4) (1,4,4,2) (1,4,4,3) (1,4,4,4) (2,1,2,2) (2,1,2,3) (2,1,2,4) (2,1,3,2) (2,1,3,3) (2,1,3,4) (2,1,4,2) (2,1,4,3) (2,1,4,4) (2,2,1,2) (2,2,1,3) (2,2,1,4) (2,2,2,1) (2,2,2,5) (2,2,3,1) (2,2,3,5) (2,2,4,1) (2,2,4,5) (2,2,5,2) (2,2,5,3) (2,2,5,4) (2,3,1,2) (2,3,1,3) (2,3,1,4) (2,3,2,1) (2,3,2,5) (2,3,3,1) (2,3,3,5) (2,3,4,1) (2,3,4,5) (2,3,5,2) (2,3,5,3) (2,3,5,4) (2,4,1,2) (2,4,1,3) (2,4,1,4) (2,4,2,1) (2,4,2,5) (2,4,3,1) (2,4,3,5) (2,4,4,1) (2,4,4,5) (2,4,5,2) (2,4,5,3) (2,4,5,4) (2,5,2,2) (2,5,2,3) (2,5,2,4) (2,5,3,2) (2,5,3,3) (2,5,3,4) (2,5,4,2) (2,5,4,3) (2,5,4,4) (3,1,2,2) (3,1,2,3) (3,1,2,4) (3,1,3,2) (3,1,3,4) (3,1,4,2) (3,1,4,3) (3,1,4,4) (3,2,1,2) (3,2,1,3) (3,2,1,4) (3,2,2,1) (3,2,2,5) (3,2,3,1) (3,2,3,5) (3,2,4,1) (3,2,4,5) (3,2,5,2) (3,2,5,3) (3,2,5,4) (3,3,1,2) (3,3,1,4) (3,3,2,1) (3,3,2,5) (3,3,4,1) (3,3,4,5) (3,3,5,2) (3,3,5,4) (3,4,1,2) (3,4,1,3) (3,4,1,4) (3,4,2,1) (3,4,2,5) (3,4,3,1) (3,4,3,5) (3,4,4,1) (3,4,4,5) (3,4,5,2) (3,4,5,3) (3,4,5,4) (3,5,2,2) (3,5,2,3) (3,5,2,4) (3,5,3,2) (3,5,3,4) (3,5,4,2) (3,5,4,3) (3,5,4,4) (4,1,2,2) (4,1,2,3) (4,1,2,4) (4,1,3,2) (4,1,3,3) (4,1,3,4) (4,1,4,2) (4,1,4,3) (4,1,4,4) (4,2,1,2) (4,2,1,3) (4,2,1,4) (4,2,2,1) (4,2,2,5) (4,2,3,1) (4,2,3,5) (4,2,4,1) (4,2,4,5) (4,2,5,2) (4,2,5,3) (4,2,5,4) (4,3,1,2) (4,3,1,3) (4,3,1,4) (4,3,2,1) (4,3,2,5) (4,3,3,1) (4,3,3,5) (4,3,4,1) (4,3,4,5) (4,3,5,2) (4,3,5,3) (4,3,5,4) (4,4,1,2) (4,4,1,3) (4,4,1,4) (4,4,2,1) (4,4,2,5) (4,4,3,1) (4,4,3,5) (4,4,4,1) (4,4,4,5) (4,4,5,2) (4,4,5,3) (4,4,5,4) (4,5,2,2) (4,5,2,3) (4,5,2,4) (4,5,3,2) (4,5,3,3) (4,5,3,4) (4,5,4,2) (4,5,4,3) (4,5,4,4) (5,2,2,2) (5,2,2,3) (5,2,2,4) (5,2,3,2) (5,2,3,3) (5,2,3,4) (5,2,4,2) (5,2,4,3) (5,2,4,4) (5,3,2,2) (5,3,2,3) (5,3,2,4) (5,3,3,2) (5,3,3,4) (5,3,4,2) (5,3,4,3) (5,3,4,4) (5,4,2,2) (5,4,2,3) (5,4,2,4) (5,4,3,2) (5,4,3,3) (5,4,3,4) (5,4,4,2) (5,4,4,3) or (5,4,4,4).

In rectilinear terms, that means a move of two cells in one dimension and one cell in at least one of the others.

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