¥(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?