From cube-lovers-errors@mc.lcs.mit.edu Fri Sep 3 13:16:50 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA19489 for ; Fri, 3 Sep 1999 13:16:49 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <002d01bee8fc$928efe80$74c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: "Cube-Lovers" Subject: Re: Rubik's Cube Perpetual Calendar Date: Tue, 17 Aug 1999 23:05:08 +0100 A calendar cube has just sold on eBay. Quite possibly it comes from the same source as the cube Chris Pelley mentioned. The description includes a picture, from which I see that it is not the same cube as the one I described on 30 July, which was bought in the UK. The eBay version uses a different type-face and uses upper and lower case for the week-day names, unlike the British version, which uses all capitals. It also has logos, whereas the British version has blanks on all faces that are not used for date markings. The British version was nonetheless a genuine Ideal cube and came in a cardboard drum bearing the title Rubik's Calendar and the copyright notice "[c-in-a-circle] MMLXXXI Ideal Toy Co Ltd, Wokingham, Berks". There are other European calendar cubes pictured on eBay which are like the British one There is something very strange about the cube in the eBay photo. In fact, I am convinced that is does not work for all dates, which drives me to the conclusion that the stickers have been rearranged. I'll explain my reasons and see if others disagree. The photo shows only one view, so we have only three faces to work on. They look like this: ------------------- | | | | | 2 | M | 5 | | V | > | < | ------------------- | | | | | J | P | 1 | | | V | < | ------------------- | | | | | Mon| P | 6 | | < | > | | ------------------- ------------------- ------------------- | | | | | | | | |Satur|day | | | 7 | A | 0 | | | | | | V | > | < | ------------------- ------------------- | | | | | | | | | F | E | B | | | C | 3 | | | | | | | V | < | ------------------- ------------------- |Rbk's| | | | | | | |Cube | | 8 | |Thurs|Ideal| 9 | | | | | | | | | ------------------- ------------------- The orientation is shown by the Vs, which point to the local upright for those markings that are not upright as shown - I've followed Dan in this. Once the markings on the various pieces of a calendar cube have been fixed, the way the cube is assembled does not matter, since to show the date we need solve only one face, and that can be done from any starting position, any necessary counterbalancing twists or permutations taking place in the other layers. Let's assume the face used to show the date is the front face. Therefore we only need to worry about what markings each piece will bear. The straightforward approach in designing a cube of this sort, it seems to me, is as far as possible to keep all the markings of the same type - that is, destined for the same position on the front face - together on the pieces carrying them. So the week-day names would be on one set of corner pieces, destined for the top left of the front face, and the numbers forming the units digit of the day of the month would be on another set, destined for the bottom right of the front face. In that way, clashes in which the piece would be needed in two places at once are avoided. If this approach is not followed, then either there must be no clash, or markings must be duplicated. An example of the first would be an edge piece that combined the F or B of FEB with the 3 of the tens digit of the day of the month, a combination that is possible because there is no FEB 30. The picture on the container of the British calendar cube, though not the cube itself, illustrates the other possibility, since one edge-piece combines J and 2. That means that JAN 20 and similar dates cannot be shown unless either the J or the 2 is duplicated. As it happens, there is one spare edge-piece face on that cube, so one duplication could be managed, but no more, but it is impossible to see from the picture if there is any duplication. Probably not, because there are some other impossibilities and inconsistencies in the pictures which suggest they show non-functioning mock-ups. The different markings that need to be accommodated on the edge pieces, defined by their position on the front face, are: Top: DAY Left: the eight initial letters of the month, J F M A S O N D Right: the ten letters completing the abbreviation for the month, N B R Y L G P T V C Bottom: the four numbers for the tens digit of the day of the month, 0 (or blank) 1 2 3. The edge-piece at the top will always stay there, since it is needed to show DAY (assuming no duplicates). So the other face of this piece will never show on the front face and cannot carry a useful marking. It can be blank, or carry a logo. In total, including the face backing DAY, we now have 24 faces, and that is exactly the number we have available if we have one face for each of the markings above. As it happens, the one letter that occurs at both the start and the end of a month, N, is symmetrical in the sans-serif typeface used, and in the British cube is made to double as a starting and an ending letter, since it can be either way up. That frees up one face to permit one duplication. It is impossible to see if the same approach is followed in the eBay cube. As a matter of interest, the British cube mostly (but not in all cases) puts an initial and a final letter together on the same edge-piece. That is possible without too much juggling to avoid the clash of having the start and end of a month on the same edge piece, but is not necessary - the principle of segregating the different types of marking would lead to four edge-pieces with the initial letters and five with final letters. If we turn back to the eBay cube, we find that the visible edge-pieces are as follows. Day/P, J?, M?, 1A, F?, 3?, B/blank, blank/? logo/?, 3x?? Since Day is combined with P, we need a duplicate of one or other if dates in SEP or APR are to be showable. But even then we would not be able to show APR 10 unless a duplicate of 1 or A was included. Thus even if one N is used for both the start of NOV and the end of JAN or JUN, we would already have one face too many. Yet on top of that there are two blanks and a logo. One blank is usable as the blank for the tens digit in dates like JAN 1, and one among the month letters is there is only one N. But that still means that there is an extra blank even if there are no duplicates. If extra blank faces are included, then other needed markings must be omitted and dates involving those markings could not be shown. In fact the only reasonable explanation I can see is that some stickers have been removed and put back wrongly. Roger Broadie