Cindy Hayes Birthday Cake Problem
presented by Art Mabbott, July 17, 2002
We have a birthday cake...a square one that is frosted on the top and the sides. We need to divide it up all of the cake exactly so that:
- Everyone receives the same amount of cake and
- Everyone receives the same amount of frosting.
- If there were four people, how could you cut the cake up?
- If there were 8 people, how might you slice it?
Are there other numbers of people for which you could slice it up and follow the rules? This is the problem for you to work on. How can you slice the square cake so that 1) everyone receives the same amount of cake and 2) everyone receives the same amount of frosting?
------- For fun Suzanne thought you might enjoy these problems -------
GeoPoW: Dissecting a Hexagonal Birthday Cake into Six Congruent Pieces
by Annie Fetter
originally posted September 2-12, 1997
MidPoW: Pi Day, Let's Eat Cake!
by Judy Ann Brown
originally posted March 13, 2000
Math Challenge #54
Cut the Cake
Some selections from the Math Forum's Ask Dr. Math Archives:
- Cutting An Equal Number of Slices of Cake [07/13/1998]
One cake is 35 slices and another is 42 slices. If the cakes need to have
the same number of slices, how many slices should they have?
- Cutting a Square [05/05/1999]
What is the maximum number of pieces that a square can be cut into with
70 straight cuts?
- Cutting a Square into Five Equal Pieces [07/12/1999]
How can you divide a square cake into five equal parts, cutting through
the center point?
- Cutting Cake with Geometry [2/4/1996]
A cake is square when viewed from the top. Height is unspecified. It is
iced on top and the four vertical sides. How can the cake be divided in 5
pieces such that each piece has the same amount of cake and the same
amount of icing? How can you minimize the number of cuts you have to make
in the cake and still meet this target? Alternatively, how can you
minimize the total length of the cuts you make in the cake?
- Dividing A Cake - A Math Puzzle [12/20/1998]
How can you cut a 9" square two-layer cake into 13 pieces so that each
piece has exactly the same amount of cake and frosting?
- Dividing a Square Cake into Five Equal Pieces [07/28/2001]
How can you divide a square-topped cake that is a rectangular solid and
is frosted on all faces into five pieces so that everyone receives the
same amount of cake and icing?