Martin may not have known the exact history. When he says `C & G later discovered ...', it was in fact JHC & Mike Guy. I was in India at the time, and constructed a SOMAP independently, tho it may not have been quite complete. We, the Guy family, were introduced to the Soma cube by T H O'Beirne, who visited us in London in the late fifties, before Mike went to Cambridge and met Conway. We had found almost all of the 240 solutions, by a random brute force search, including the `oddball' one, which was found by my wife Louise. At that stage Mike went to Cambridge, met Conway, and they systematized and completed the enumeration, as described in Winning Ways. One of many `in' jokes of Winning Ways is found by looking up Peter Guy in the Index. (This should be p.843, not 841, in the recent edition.) You won't find anything there, but he is responsible for the `official colors' of the 7 pieces. At the time a keen aircraft model maker, he got the job of painting the pieces of the puzzle that I made. It was serendipitous that he colored the two enantiomorphic pieces Red and bLue, which are `official names' of the two players, Right and Left, in many parts of the book. R. On Fri, 13 May 2005, ed pegg wrote:
Martin Gardner's Mathematical Games The Entire Collection of his Mathematical Games Columns
is now out! I got my copy in the mail today. The CD has all 15 books, and is fully searchable. I just tried a search on "Richard Guy" -- and now I'm copying a paragraph.
Martin Gardner wrote: Conway and Guy later discovered that if you begin with any of 239 solutions (one solution is an anomaly), all of the others can be obtained in 238 steps by altering the position of no more than three pieces at each step. Conway has drawn a large graph (which he calls the Somap) showing how the 239 solutions are linked to one another and giving each solution a concise notation, called its "somatype." The map does not give any one solution, but once you have built the cube in any of the 239 ways, the map enables you to transform it to all the others by moving two or three pieces at a time. The map is too complex to reproduce here, but you will find it on pages 802 - 803 of Winning Ways, Vol. 2, by Elwyn R. Berlekamp, John H. Conway and Richard Guy (Academic, 1982).
That's pretty handy! Many thanks to all involved for putting the collection together the first time around, those who assisted in getting the books out, with correction and commentary, and those who helped to get the CD finalized.
You can get the CD at http://www.maa.org/ . Well, actually, right now, you can't -- the bookstore website seems to have gone down. It's always something. When it's up again, you'll be able to order you own copy.
Ed Pegg Jr
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun