Question 19
The figure below, not drawn to scale, is formed by combining two types of triangles. Triangle 1 and 2 are isosceles triangles each with a $30^\circ$ angle at one of its vertices. Triangle 3 is a right-angled isosceles triangle. Triangles 4 and 5 are isosceles triangles each with a vertex of $30^\circ$. Triangle 6 is a right-angled isosceles triangle. This pattern continues with subsequent isosceles triangles. Given that the $n$th triangle overlaps with Triangle 1, find the smallest possible value of $n$.
