From ncramer@bbn.com Thu Jul 29 09:40:49 1993 Return-Path: Received: from LABS-N.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA22477; Thu, 29 Jul 93 09:40:49 EDT Message-Id: <9307291340.AA22477@life.ai.mit.edu> Date: Thu, 29 Jul 93 8:59:44 EDT From: Nichael Cramer To: "Ronnie B. Kon" Cc: Cube-Lovers@life.ai.mit.edu Subject: Re: Hint wanted for 4x4x4 Hi Ronnie Let me try to restate the problem slightly to make sure we are talking about the same problem. Basically, you can solve the entire cube, except that the pieces "1" and "2" in the diagram are flipped/exchanged: XXXX XXXX XXXX X12X Assuming this is the problem, the hint is as follows: The problem here is that some of the face pieces are not really in their right places. In short, one of the center slices is 1/4 turn out of phase. The simplest way to proceed (at least for me) is to move to the following state: XX2X (i.e. rotate one of the central slices 1/4 turn) XXOX XXOX X1OX ^ | Now, you can solve for pieces "1" and "2" and --using these pieces as a landmark-- proceed from there. Hint #2: You can help avoid this problem by solving the face pieces last. Extra Credit: Actually, the state as shown in the first diagram above is pretty interesting in that the analogous position on a 3X3X3 cube (i.e. a single flipped edge cube) is of course impossible.