2024 Gauss 8 Problem 17

The Gaussbot factory assembles robots. Each robot comes in one of three colours: red, blue, or green. Each robot also has a number stamped on its head: 1, 2, 3, or 4. The nth robot assembled is the first robot to have the same colour and the same number as a previously assembled robot. What is the greatest possible value of n?

\textbf{(A)}\ 11\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 13\quad \textbf{(D)}\ 7\quad \textbf{(E)}\ 8

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 Gauss contests here.