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There are two types of aproaches to what can be meant by total

(or maximal) randomizing. One is to consider states of the cube that

are maximally far away from being solved (that is the minimal number of

quarter twists needed to solve from a given state is maximallized.

the other, which may be more useful for making the cube more difficult

to solve, is based on maximallizing the amount of time it would take

a person (or a program, for that matter) to solve the cube. Of course,

since this amount of time is both dependent on the state of the cube, and

how the person (or program) goes about solving it. Thus the set of most

randomized positions is dependent on who is solving the cube.

the advantage of the first definition is that it seems to be of more

theorectical significance (the number of quarter turns needed to

solve from this position gives you the diameter of the state graph).

The second approach seems more kludgy since it much less well defined

since the amount of time it takes to solve the cube if a function of

many variable besides simply the initial state.

This distinction is much like differing strategies for writing chess

playing programs, you could write it assuming the oponent to be a

"perfect" player (as if a complete look ahead to the leaves of the tree

appraoach were being used by the oponent) or by considering how the

oponent is likely to play (have the program try to confuse the oponent

by taking advantage of something that the oponent wont recognise).

the second method thus will take into account the knowledge-base

available to the solver (for example trying to trick the solver into

thinking that the cube is in one of the easy to solve classes but really

isnt, thus leading the solver down a blind alley)

This gives me an idea for a game where oponents are each trying to bring

a randomized cube into two different final states (each of which

is hopefully equally far away from the initial state, just to make the

game fair) by alternately taking turns making quarter turns. of course

one must make up some rules so that that the game terminates (ei going

around cycles in the state graph an indefinite number of times is

disallowed), and these rules might not be very obvious,although

they would prob be similar to some of the stalemates rules of chess.

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