Terence TaoRE: https://mastodon.social/@ZachWeinersmith/116375447678097912
This was a fun collaboration! See also the crypto challenge at the end of the final strip in the 5-part series.
robinhouston
Mark Dominus@robinhouston I didn't give it any thought, but when I read it what I imagined was polyominoes made of regular triangles, of size 6n, and whether they could tile a hexagonal region of a triangular grid. I have no idea if this was what was actually meant.
But I have looked at the analogous question about what sizes of triangles can be covered by 3-hexes, and it was interesting.
novalis@mjd @robinhouston Those are called "polyiamonds", which must have been what was meant; I think it's false because of polyiamonds with holes.
@novalis @robinhouston Thanks, I couldn't remember the name. I assumed they meant simply connected ones.
@mjd @robinhouston I think there's still a problem with long spiky caltrop shapes.
@novalis @robinhouston Good point, if it has two long arms that almost encircle a bay but that leave a narrow inlet, it clearly won't cover the plane or any other large region of interest.