Two players take turns marking the edges of a complete graph \(K_n\) , for some \(n\), with + or -signs. The two players can choose either mark (this is known as a *choice* game). In Positive Triangle, the first player to complete a triangle with an even number of – signs is the winner. In this game, the goal or winning triangle can contain marks made by both players.

- Under what conditions does the first player win?
- If the first player to create a positive triangle loses, under what conditions does the first player win?
- For which complete graphs is a draw (no winner) possible