Hello,

It has been pointed out in various posts that the principle that is known to magicians / mentalists as "Gray code" actually does not refer to the Gray code, but rather to De Brujin sequences.

Anyway - I wonder whether there are also tricks that *are* actually based on the mathematical principle of the Gray code. Does anybody knows one?

Same question for error-correcting codes (such as the Hamming code). I am aware of an example for a trick for error-correcting code by Todd Mateer, described at https://mthsc.clemson.edu/misc/MAM_2014/doublemagic.pdf. Are you aware of others which are a little more elaborated?

Thanks,
Ralf

A comprehensive listing of such effects (60 Entries!) can be found here: http://archive.denisbehr.de/list/category/519

I haven't looked into them, so I wouldn't be surprised if you find some that are DeBrujin sequences in that list.

Thank you! I already knew this link, and actually all references from Denis' list that I had access to deal with De Brujin sequences. My question was in the different direction: Are there effects that are NOT based on De Brujin, but actually on the Gray code?

Thanks,
Ralf

In the meantime, I did some more research, and here are the results (just in case somebody will find this thread in the future):

Diaconis and Graham write in "Magical Mathematics" with respect to Gray codes: "But as far as we know, there has never been a single use in magic." I can only agree with their following sentence: "Now there is a magic problem!"

Applications of the Hamming code for two-person telepathy can be found in chapter 12 of "Mathematical Card Magic" by Mulcahy. While the effects seem to be less suitable for a performance, they can be used as a nice illustration for teaching coding theory.