Consider an equilateral triangle. We wish to tile it with n congruent triangular tiles. We will call such a triangulation a CT-n tiling. Clearly there is a CT-n tiling if n = 2 (two 30-60-90 right triangles), n = 3 (three 30-120-30 isosceles triangles) or n = 4 (four equilateral triangles).

(1) Show that there is a CT-n for the following values of n: 1,2,3,4,6,8,9,12,16,18.

(2) Find 4 infinite sequences of n such that there is a CT-n for all values of n in the sequence. (The sequences may not overlap.)

Unsolved (by me) problems

(3) Find (with proof) at least one value of n for which there is no CT-n.

(4) Determine exactly which values of n yield a CT-n.