Recently at Girls’ Angle, we brought in a brownie and told the girls that nobody could have any until they figured out a way to dissect it so that everyone gets an equal share.
I’ve done this activity before, but this time, there was extra special incentive because the brownie was baked to scrumptious perfection and donated by Petsi Pies, a wonderful bakery here in Cambridge (who, by the way, take advantage of the irrational nature of for their annual Pi Day contest). Because of this extra inducement, I gave our members an extra challenging problem:
On a coordinate plane with each unit representing 1 inch, the shape of the brownie was a quadrilateral whose vertices could be placed at (0, 0), (0, 12), (16 2/3, 0), and (14 3/8, 11 1/2).
How can you split this brownie fairly into 19 pieces?
There are really infinitely many solutions, so one could toss in the practical condition that the cutting scheme be easy to realize with a kitchen knife.
I’ll describe a solution our members came up with in the next issue (Volume 5, Number 4) of the Bulletin. Until then, you’re welcome to send yours to girlsangle “at” gmail.com.
If you’re interesting in doing this activity for other class sizes and are having trouble coming up with an interesting brownie shape, I made a few suggestions in Areas and Brownies which appeared in the January 1997 issue of Mathematics Teaching in the Middle School.