Some tessellated pantomimes - anyone would think that they've been reading my blog.
As I mentioned in my previous post, depending on your point of view about rotation, there are either 12 or 18 distinct pentominoes, and similarly depending on the classification, the St Pancras tessellation uses either one or two different tiles in the shape.
This gets me to thinking, I wonder how many of the pentominoes successfully tile the plane, and it seems to me that to do this properly, rotation shouldn't be allowed, so the St Pancras arrangement doesn't count, and the question should be considered as a score out of 18.
The answer may well be in Marcus du Sautoy's Finding Moonshine, but I'm not going to look there, I'm going to have a little think about it (and may have to ask Nicky if I can have some of her squared paper to try things out)!
The answer is definitely at least one (tiling with a 5x1 tile seems pretty easy!) but less than 18 (can't picture a way in which the 'U'-shaped pentomino will tile). I'll get back to you on a more exact answer sometime.