Yes, Andy missed something because I did. Find all pairs (T,N) such that T is a right triangle and there exists a tiling of T by N congruent right triangles similar to itself. --Dan P.S. Er, multitasking made me do it. On 2014-02-10, at 1:46 PM, Andy Latto wrote:

I must be missing something; can't you dissect *any* triangle into 4 congruent triangles, each similar to the original, by joining the midpoints of the sides?