When I was in high school, the Rubik cube was a bit hit.
I got one around 1980. A colleague and high school friend of mine, Christian
Styger found a solution strategy earlier than me. It took me
longer. My own solution was not a very efficient solution, it allowed to solve
the cube in about 30 seconds if lucky and the cube was lubricated.
I just found in old high school math diary books an old document from this time in which
I wrote down my solution in high school (written on a type writer).
Note that at that time, we would find the solution on our own without any help nor
by consulting with an other person or any solution manuals. This took about 3 weeks for me, pondering the
problem for certainly over 100 hours of trial and error, sometimes even dreaming
about the problem, carrying the cube constantly with me, even while walking. The
hardest thing was to find combination moves which affect only one layer while fixing
the other two. The notes contains also some ideas about a 4-dimensional Rubik cube.
[By the way, a episode of an other puzzle is mentioned in the 2005 version of
my multivariable Chinese remainder theorem.
That 2005 version is still accessible
here as a PDF and was
also part of a Talk (PDF)
at Brandeis. Page 7 in the 2005 text
contains for the ``Zauberkugel" story. By the way, I had tried in 2005 and in
2012 to submit that result to a journal but referees always found it too trivial (or assumed
it is well known). This was a bit annoying as most of the work in such a case is not the discovery
but actually do the literature research about where it could already have been appeared. Somebody managed to
publish such a result
eventually. In retrospect, my 2005 version has been an original new
discovery, which is surprising given how old the Chinese remainder theorem is. A bit surprising
is also how the 2015 article does not mention my preprints, even so at that time, googling
``multi-variable Chinese remainder theorem" would lead to the 2012 paper.
I also had refereed that article from that author once in 2013 when it was under consideration
for publication in the American Mathematical Monthly and I had pointed out my result.
The author must definitely have been aware of it. I in 2012 thought to wait an other 7 years for an new
attempt but having the result published now would defeat the purpose.]
Here is the PDF. And here are the pages:
Oliver Knill, Posted May 14, 2020,