Single Comment

If only the Basilisks complicate matters (and not the relative order of
other pieces), then at worst you need to consider every ordering of
Basilisks and decide whether each other piece is moved before, between, or
after them, which is 2 * 3^6 = 1458 combinations.  With one adjacent
Basilisk, the worst case is 2^7 = 128.  I suspect that's plenty small to
brute force.

But if you want to be clever, I believe the only times order matters are
when a Basilisk sees a pushed piece's destination before the Basilisk
moves (so it petrifies that piece only if moved second), or when it sees a
pushed piece's origin after the Basilisk moves (so it petrifies that piece
only if moved first).  So you can list all the potential interactions where
order matters:

Basilisk N relative to NW and NE
Basilisk S relative to E and W
Basilisk E or W relative to N
Basilisk SE or SW relative to S
(A Basilisk NW or SW would petrify the Go Away and prevent it from
screaming.)

Where N (north) is the average direction of the Basilisk's Knight moves;
so with a Go Away on e4, an Alabaster Basilisk on e5 is 'north' and so
order-dependent with d5 and f5, but an Obsidian Basilisk on e5 is 'south'
and so order-dependent with d4 and f4.

So the order of the Basilisk only matters relative to at most 2 other
pieces, giving at most 8 permutations in the worst case (there's only one
case where both Basilisks affect the same pieces, and in that particular
case you might as well move the Basilisks simultaneously).