2018 Pascal Problem 22

A Miniou circuit contains nodes and wires and obeys the following rules:

- Each wire connects two different nodes. - There is at most one wire between each pair of nodes. - Exactly three wires are connected to each node.

An example of a Miniou circuit is shown. If a Miniou circuit has 13\,788 wires, how many nodes does it have?

\textbf{(A)}\ 9190\quad \textbf{(B)}\ 9192\quad \textbf{(C)}\ 9188\quad \textbf{(D)}\ 9186\quad \textbf{(E)}\ 9184

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 Pascal contests here.