Math in the Middle Institute Partnership
Date of this Version
12-2007
Abstract
The Polygon Game ‐ Take a regular, n‐sided polygon (i.e. a regular n‐gon) and the set of numbers, {1, 2, 3, …, (2n‐2), (2n‐1), 2n}. Place a dot at each vertex of the polygon and at the midpoint of each side of the polygon. Take the numbers and place one number beside each dot. A side sum is the sum of the number assigned to any midpoint plus the numbers assigned to the vertex on either side of the midpoint. A solution to the game is any polygon with numbers assigned to each dot for which all side sums are equal, i.e. for which you have equal side sums. The most general problem we might state is, “Find all solutions to The Polygon Game.”
Comments
In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics. Jim Lewis, Advisor December 2007