From dik@cwi.nl Wed Jul 28 20:17:38 1993 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA01767; Wed, 28 Jul 93 20:17:38 EDT Received: from boring.cwi.nl by charon.cwi.nl with SMTP id AA06051 (5.65b/3.8/CWI-Amsterdam); Thu, 29 Jul 1993 02:17:27 +0200 Received: by boring.cwi.nl id AA08740 (4.1/2.10/CWI-Amsterdam); Thu, 29 Jul 93 02:17:25 +0200 Date: Thu, 29 Jul 93 02:17:25 +0200 From: Dik.Winter@cwi.nl Message-Id: <9307290017.AA08740.dik@boring.cwi.nl> To: Cube-Lovers@life.ai.mit.edu, ronnie@cisco.com Subject: Re: Hint wanted for 4x4x4 > I've been beating my head against the order 4 Rubik's cube for long > enough, and I want a hint. (Not a solution--I have a solution book if > I wanted to use it). Yes, it is not really simple. > ... > I tend to solve using commutators, but I don't see a way here. The > move I use on the top moves the marked pieces clockwise (this pattern > . . 0 . > . . . . > . . . 0 > . 0 . . > rotates and reflects, of course). There is no way to combine these > into a pair exchange (after doing the move, you still have two pieces > out of place--nothing changed from the original). Still you are halfway there if you are willing to forgo the pattern of the centers (which can always be done later). Turn the front face (at the bottom in the frawing), the right face and the back face one quarter turn before your turn, and back after. Observe that that constitutes a cycle of three edge cubies in a single middle slice. Combine with a quarter turn of that middle slice. > So, what am I missing? As I said before, I really just want a hint > here. I hope that is enough of a hint and not enough of a giveaway. (I thought there was a shorter sequence, but I disremember at the moment.) My solution for the 4x4x4 always was: first corners, next edges and finally centers. Because there are many identical pieces for the centers those are reasonably simple. It would be much more difficult if each center had its own place. dik -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland home: bovenover 215, 1025 jn amsterdam, nederland; e-mail: dik@cwi.nl