September 6, 2004
Problem of the Month

The Coconut Cake Problem

One day, my son-in-law Eric brought home a coconut cake and announced that he wanted a piece of cake with the most icing (meaning a corner). The cake was a square cake 6"x6" and 3" tall with icing on the four sides and the top. Consider the thickness of the icing to be negligible.

We decided to cut the cake in four pieces of equal volume so that my son-in-law could have the most icing. We made six cuts shown in red in the diagram below:

Determine how far in from the side of the cake that the cuts should be made. How many more square inches of icing will Eric get than each of the rest of us? (Yes, Eric really cut the cake this way!).

Solution to the Problem:

The cuts should be made .4019 inches from the side of the cake. Eric got 72 square inches more of icing than each of the rest of us.

The first part of this problem can be found by changing this to an area problem and considering just the 6"x6" square (since the depth is always three inches).
The total area of the top square is 36 square inches.
Each person should get 9 square inches of cake on the top.

See the diagram below.

My son-in-law's piece of cake had 81 square inches of icing (9 sq. in. + 4 x 6" x 3");
each of the rest of us had 9 square inches of icing.

Correctly solved by:

1. Larry Schwartz	Trumbull, Connecticut
2. James Alarie	University of Michigan -- Flint, Flint, Michigan
3. Chris McCormick	Virginia Tech, Blacksburg, Virginia
4. Walt Arrison	Philadelphia, Pennsylvania
5. John Funk	Ventura, California
6. David & Judy Dixon	Bennettsville, South Carolina
7. S. McCann	----------
8. Kevin Jacobson	Columbus, Georgia
9. Jeffrey Gaither	Winchester, Virginia
10. Misty Carlisle	Winchester, Virginia
11. Misty Carlisle	Winchester, Virginia
12. Tristan Collins	Winchester, Virginia
13. Viktor Logrell	Tullängenskolan, Örebro, Sweden
14. Bahadir GüngÖr	Tullängenskolan, Örebro, Sweden
15. Sanna Lejegren	Tullängenskolan, Örebro, Sweden
16. Emily Auerbach	Columbus, Georgia
17. Josh Feingold	California Institute of Technology Pasadena, California
18. Gustav Nilsson	Tullängenskolan, Örebro, Sweden
19. Daniel Kvist	Tullängskolan, Örebro, Sweden
20. Erik Hultgren	Tullängskolan, Örebro, Sweden
21. Jonathan Jansson	Tullängen, Örebro, Sweden
21. Jonas Sutinen	Tullängsskolan, Örebro, Sweden

Send any comments or questions to: David Pleacher