[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: