The blocks world is an old and well$-$known Al task$-$planning domain in which a robot arm manipulates blocks within a bounded workspace. Our

version of the blocks world, which we call the $"(n,k)$ blocks world", has a table$-$top with $n$ locations $\{L_1,dots{L}_n\}$ where $k$ distinct blocks

$\{B_1,$dots,$B_k\}$ can be placed and stacked in various ways by the robot.

A state in the $(n,k)$ blocks world is denoted as a list $S=[S_1,dots{S}_n],$ where $S_i$ is the list of blocks stacked at $L_i,$ with the top block first in

the list is an empty list $[$