distributed BFS

lets say there are n computers, C(1), ..., C(n)
load 6gb of table space into each one

start:

on C(k), loop i=(6e9)(k-1) to (6e9)k-1
 decode i, apply move, encode puzzle into new number j
 if (6e9)(k-1) <= j < (6e9)k, update the table as normal
 else, find the integer k' such that (6e9)(k'-1) <= j < (6e9)k' and append j to the list l[k']
save each list l[r] to a file "ck_cr.txt" (a "communication file" from computer k to computer r)
wait for every computer to get to this point

on C(k), loop through the files "ci_ck.txt" for all i=1..n where i!=k
 for each number in the file, set the corresponding value in the table to the right depth
 delete "ci_ck.txt"
wait for every computer to get to this point

goto start