Talk:Sphinx tiling

Not just 4 and 9
I've found it's possible to tile the sphinx tile with 25 or 49 copies of itself. I believe it's possible to do with any n2 value. 16 is trivial, just do the 4-tiling twice. Likewise for 36 (tile by 4 and then by 9, or vice versa), 64 (tile by 4 three times), 81 (tile by 9 twice), 100 (tile by 4 and then 25 or vice versa) and by extension any square of a number with 2, 3, 5 and/or 7 as factors. I haven't yet found an 112 tiling, though I suspect it's probably possible. Not sure how one would go about proving that it's possible for any n2... Lurlock (talk) 22:30, 30 October 2015 (UTC)


 * I've proven the 112 tiling for this, see [], which also shows my solutions for 52 and 72. Also per that discussion, there's apparently a paper out there that proves my theory that it works for all n2, though not available online.  I haven't seen it, so can't comment, but if that's the case it probably should be stated in this article.  At the very least, we know for sure that 22 and 32 (and their multiples) are not the only possibilities, as I've found 52, 72, and 112, so thus any square of a number that has 2, 3, 5, 7, and/or 11 as prime factors are definitely possible. Lurlock (talk) 17:39, 13 November 2015 (UTC)
 * As I wrote at Talk:Rep-tile, the result that any square number of sphinxes can tile a sphinx has been published this year in a paper at JCDCG. (The paper shows more strongly that the number of tilings grows quickly.) —David Eppstein (talk) 18:38, 13 November 2015 (UTC)
 * Yes, I was just making sure it was noted here so that the article can be updated at some point. It still only mentions the rep-4 and rep-9 tilings.  I've proved that there are more, but I'm not published and reviewed, etc., so I can't add it to the article without falling under "Original Research".  If you could add it with the proper citations and all, that would be great, since I don't have access to your source. Lurlock (talk) 23:39, 13 November 2015 (UTC)