2021 Fermat Problem 23

In Figure 1, three unshaded dots are arranged to form an equilateral triangle, as shown. Figure 2 is formed by arranging three copies of Figure 1 to form the outline of a larger equilateral triangle and then filling the resulting empty space with 1 shaded dot. For each integer n > 2, Figure n is formed by first arranging three copies of Figure n - 1 to form the outline of a larger equilateral triangle and then filling the resulting empty space in the centre with an inverted triangle of shaded dots.

The smallest value of n for which Figure n includes at least 100\,000 shaded dots is

\textbf{(A)}\ 8\quad \textbf{(B)}\ 9\quad \textbf{(C)}\ 10\quad \textbf{(D)}\ 11\quad \textbf{(E)}\ 12

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.