Category Archives: Positive Triangle

Positive Triangle Game

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.

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

positivetriange