K Septyn
United States Unspecified Michigan
SEKRIT MESSAGE SSSHHHHHHHHH

I happened to bump into Hexadoms while looking for another game, but dominostyle games always seem to catch my mathematical eye, and this one was no different. At BGG I didn't see any indication of how many tiles were in the set, so the puzzle became one of finding that number.
The pictures I found show the hexes are divided into 6 triangular areas (sextants?), and opposite areas have the same number. This seemed like a good rule to observe, as it would keep the number of tiles reasonable. The pictures don't show anything that would indicate a "starting" or otherwise unique area, so rotational symmetry would also keep the number low.
If there were a unique area, the number of tiles in a 3high set (like the one pictured) would be (3+1)^3 = 64. This seems too large for the size of the package, and there's no sign of that unique area anyways.
I wanted to see if there were any special rules visible in the tiles that would restrict their ordering. For example, TriOminoes requires the numbers increase as they are listed clockwise around the tile, same for QuadOminoes. Some Google searches found a picture of a full faceup setthere are 24 tiles total. The puzzle was solved....
But 24 tiles seems like a small number for a dominolike game. Sure, a traditional double6 set of dominoes has 28 tiles, but a double9 set has 55, and the TriOminoes set ("triple5") has 56. How much bigger could a "triple4" set of Hexadoms be?
The picture showed there wasn't any apparent restriction on number placement: the set contains both "012" and "021". That would make the math a little easier.
I'll skip the math discovery phase to say there is a formula for determining the number of tiles in a triplen set of Hexadoms. It's identical to the "number of ways to color vertices of a triangle using

K Septyn
United States Unspecified Michigan
SEKRIT MESSAGE SSSHHHHHHHHH

...and of course, the rest of the post was deleted in transit due to a lessthan sign. Yay.
The Online Encyclopedia of Integer Sequences (OEIS) lists this particular sequence as "A006527". This is "Number of ways to color vertices of a triangle using <= n colors, allowing only rotations." That makes sense given we're dealing with the rotation of a duplicated 3number set.
My earlier post was a little more wordy, but I'm going to sum up:
The formula for tiles in a Hexadom set is (x^3 + 2*x)/3, where n = highest number in the set and x = n + 1. For example, the published game is a triple3 set, 3+1 = 4, and 4 into the formula gives 24 as the answer.
A triple4 set of Hexadoms doesn't seem too unwieldy, it's only 45 tiles total. The triple5 set isn't bad either at 76 tiles (less than the 91 of a double12 domino set), but a triple6 set would need 119 tiles (one less than a double14 domino set), and I think that's going to be way too many hexagons for the average domino player.


