From:

Subject:

In response to a note of mine,

A search treegiving distances from Start calculates d(I,IY) for all

positions IY in the domain of inquiry. With an X-rooted tree,

distances are of the form d(X,XZ) for all positions XZ in the domain

of inquiry. In general, it is not the case that d(I,IY)=d(X,XY).

whereupon what's-his-name :-) responds

In this notation, it is certainly true that

d(<id>,<h>) = d(<g>,<g><h>). This is because each process that

transforms <id> to the state <h>, will also transform <g> to <g><h>,

and likewise each process that transforms <g> to <g><h> will also

transform <id> to <h>.

This is what I was trying to say in the message that started this: that

one is building a tree of all move sequences no longer than N, which is

to say a certain subset of permutations of the cube. But these

permutations can be applied to arbitrary positions just as well as as

they can be to Start. Any Cubist knows this; it's the basis for many

of the common solving macros: that a process that (say) swaps RF and

RB, and TF and TB, can be used to swap whatever cubies happen to be in

those cubicles, even if they aren't the RF/RB/TF/TB cubies.

der Mouse

mouse@collatz.mcrcim.mcgill.edu