Let T(n) denote an equilateral triangular board with side length of 2^n units, subdivided into 4^n equilateral triangles with side length of one unit each. A trapezoidal tile (or triangular triomino) is a tile consisting of 3 adjacent equilateral triangles, each with side length one. (See picture in the textbook on page 277)
Prove, using mathematical induction, that if any corner triangle is removed from a T(n) then the rest of the triangular board can be tiled using trapezoidal tiles for any positive integer n.
Use part (a) and mathematical induction to show that if all three of the corner triangles and one additional triangle is removed from T(n) then rest of the triangular board can be tiled using trapezoidal tiles for any positive integer n.