The 4 compound leapers I'd like to look at are:
(1,2), (0,2), (1,1); knight+kirin
(1,2), (1,3); knight+camel
(1,2), (2,3); knight+zebra
What arrangement of 8 of each of these 4 compound leapers (a total of 32 pieces) has the "strongest coverage properties" on a 16x16 board, defined as such?:
- Any square that a piece can attack is counted as being covered once per piece
- A square occupied by a piece is not covered by the piece occupying that square
- Sort first by # of squares covered once; then by 2x, 3x, up to highest cover count
For example, an arrangement of pieces that covered 256 squares at least once each and covered 96 of those squares at least twice each would by this definition be considered "stronger" than an arrangement that covered 252 squares once and 112 squares twice; the higher at least twice-covered square count doesn't matter if it covers less squares at least once each, and so on.
If any riders were in the mix (rooks and bishops are examples of rider pieces; rooks the (0,1) rider and bishops the (1,1) rider), I would add that "a square that a rider's path to is blocked is not covered by that rider"; my intention is for this definition to be generalized to any combination of pieces on a board of any dimensions.
(I should double-check; is this "strongest coverage arrangement" I'm defining already a thing which there is another name for?)