Pentimo, Afterthought

While (finally) getting set to order a test sample of Pentimos, a curious thing occurred to me: I did not even contemplate using zero pips as a facet value!

Confronted by this realization, I sat down and crunched some quick numbers, and found it was impractical to add a 4th value to the pentimo set: Currently, there are 51 individual tiles in a Pentimo set. Adding a null set and including all permutation, I get 1024 combinations, removing the 4 unique solutions (0,0,0,0,0; 1,1,1,1,1; 2,2,2,2,2; & 3,3,3,3,3) leaves 1020 combinations, which can be divided by 5 to eliminate radial redundancy (i.e. 1,0,0,0,0; 0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; & 0,0,0,0,1), leaving 204 variations, for a total of 208 total tiles.  Frankly, 208 tiles would be both costly to make, and impractical to play with...

So, omitting the zero-set was actually a good choice, but for some reason, it was an option that just never came to mind when I was in the midst of the design process.