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)[reply]

I've proven the 11² tiling for this, see [[1]], 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)[reply]

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)[reply]

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)[reply]