Trenkler must be using a different definition of Magic Cube. [Some older books only require the magic sum for the exterior face diagonals, etc.] Martin Gardner published my proof of non-existance of a magic 4^3 in Scientific American c. 1974. The non-existance of 2^3 is trivial, and non-existance of 3^3 is easy. The 5^3 must have its average value in the center, similar to the 3^2. This prevents 5^4. Trump & Boyer constructed 6^3 and then 5^3 a few years ago, using a mix of cleverness & computer search. 7^3 and larger is apparently very old news. Boyer has a web page about the 5^3 and 6^3; I think it's multimagie.com, and covers a lot of different kinds of magic objects. He's on Math-Fun, so he'll likely contact you directly. I've worked on showing non-existance of 6^4 from time to time, without success. I have a complicated sum-restriction for 6^3, but it (obviously) doesn't preclude them. Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] On Behalf Of Ed Pegg Jr [ed@mathpuzzle.com] Sent: Friday, March 07, 2008 9:41 AM To: math-fun Subject: Re: [math-fun] Magic cubes MathWorld Headline News Perfect Magic Cube of Order 5 Discovered By Eric W. Weisstein November 18, 2003--This week, German mathematics teacher Walter Trump and French software engineer Christian Boyer announced the discovery of a perfect magic cube of order 5, thus settling the long-standing question of the existence of such a cube. http://mathworld.wolfram.com/news/2003-11-18/magiccube/ Richard Guy <rkg@cpsc.ucalgary.ca> wrote: I have a question in UPINT, D15: ``Has anyone constructed a 5 x 5 x 5 magic cube, or proved its impossibility'' (just possibly asked by Rich Schroeppel?). I've recently downloaded a 2-page article by Maria'n Trenkler, An algorithm for making magic cubes, which was evidently published in Pi Mu Epsilon J, 12 #2 (Spring 2005) 105-106. It produces magic cubes of any order > 2. Am I the only person not to know about this? R. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun