From cube-lovers-errors@oolong.camellia.org Tue Jun 3 14:52:43 1997 Return-Path: cube-lovers-errors@oolong.camellia.org Received: from oolong.camellia.org (localhost [127.0.0.1]) by oolong.camellia.org (8.6.12/8.6.12) with SMTP id OAA01658; Tue, 3 Jun 1997 14:52:42 -0400 Precedence: bulk Errors-To: cube-lovers-errors@oolong.camellia.org Message-Id: <199706031013.GAA17406@life.ai.mit.edu> Date: Tue, 03 Jun 1997 06:13:22 EDT From: Richard M Morton RMM - ICOMSOLS To: cube-lovers@ai.mit.edu MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Subject: Number of States for 2x2x2 cube ------------------------------------------------------------------------------- Reading about the number of possible states (88million) for the corners of the 3x3x3 cube (equiv. to 2x2x2) made me try working this out for myself. My logic was : Cube has 8 corners, each of which can have 3 orientations. Number of possible states is (8*3)*(7*3)*(6*3)*(5*3)*(4*3)*(3*3)*(2*3)*(1*3) = 8!*3**8 = 264,539,520 This figure of course includes some states only possible by disassembling the cube (or maybe by twisting it in a fourth dimension ?). Without this the last corner can only have one orientation so the number of states achievable by twisting only in 3d is 8!*3**7 = 88179840 I assume that this is the correct figure but what I would like to know is whether my logic is correct ie is the assumption about the last corner being fixed in orientation the only requirement (I am not a mathematician so please excuse me if this is obvious). Richard Morton "I'm Brian and so's my wife"