The Triangle Game
A “Habits of Mind” Problem
(Paul Sally, U. Chicago) Consider an equilateral triangle with points located at each vertex and at each midpoint of a side. The problem uses the set of numbers {1, 2, 3, 4, 5, 6}. Find a way to put one of the numbers on each point so that the sum of the numbers along any side is equal to the sum of the numbers along each of the two other sides. (Call this a Side Sum.)
Is it possible to have two different Side Sums?
What Side Sums are possible?
How can you generalize this game?