From:

Subject:

I do not follow the reasoning. It seems quite possible that there is a

non-symmetric local maximum. In any case, it is not a definition, but rather a

proof that needs doing. It is certainly true that a move from a non-symmetric

configuration will either

a. get closer to home

b. stay the same distance from home

c. get further from home.

Furthermore, it is obvious that there are usually both (a) and (c) cases. What I

don't see is the argument that there must always be a (c) case.

One way of looking at it is that there is an enormous graph connecting all

solutions by one QTW moves. Nearly all nodes are non-symmetric. You argue

that from every non-symmetric node there is a move to a node that is further

from home. I am willing to be convinced, but am not yet, and mere probability

favors the following:

Conjecture: There exists a non-symmetric configuration from which every move

leads to a position that is closer to home.

Bill