If you color equilateral triangles with n colors at the three sides you get
(n^3+2n)/3 one-sided and (n^3+3n^2+2n)/6 two-sided
distinct pieces. In 1929 MacMahon suggested the pieces and in 1971
Philpott asked for
sets, which can fill a triangle. Possible values for n are 1,2,24 and a finite set of numbers
above 5000. So far I haven't seen a solution for n=24, but here is one.
If you'd like to solve a smaller puzzle by hand, you can choose a version with 24 pieces and
three different edge types from Gamepuzzles.
