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Fair slices (Posted on 2018-01-16) Difficulty: 2 of 5
The 3 kids are going to split a small square cake. It would be easy enough to cut it fairly into thirds but there is a catch:
It is frosted on the top and four sides and they each want to make sure they get a fair share of cake and frosting.

Find one or more simple (or complicated, creative, etc) ways to accomplish the task.

I offered to slice it into fourths and take one as a 'slicing fee' but that didn't go over well.

No Solution Yet Submitted by Jer    
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cake plus frosting | Comment 2 of 8 |
If you make all the cuts vertical you can treat the cube as a square.

Pick three points so that the perimeter is cut in thirds, then cut from those points to the center.  For example, choose one point at the NW corner, another 1/3 of the way S of the NE corner, and the third 1/3 of the way E of the SW corner.

Each kid gets 1/3 of the cake and 1/3 of the frosting on top.  Two kids get all the frosting on one side and 1/3 of the frosting on another side, while the remaining kid gets 2/3 of the frosting on two sides, each totaling 4/3 of the side frosting.

Every kid is content with the allocation and equally full of cake and frosting.  Peace reigns in the household.  

It's tougher to prove but I believe that the cuts from the center don't have to be straight lines.  As long as the cuts are congruent the result is the same.  So arcs or zigzags or a series of alternating semi-circles would work as well.

Edited on January 16, 2018, 10:13 am
  Posted by xdog on 2018-01-16 09:21:23

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