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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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Other, more complex solutions | Comment 6 of 8 |
Square= ABCD
BM=1/3BC
AN=2/3AD

A------N--D
|                    |
|                    |
|                    |
B--M------C

AREA ABM = AREA CDN = 1/6 AREA ABCD
AREA AMCN = 2/3 AREA ABCD

Divide AREA AMCN in four pieces, each one misuring 1/4 of  the area AMCN, and so that AN is on one piece and MC is on another. Pieces including AN and MC are assigned to kid 1. 

Kid 2 has ABM and the half of the area AMCN not assigned to kid 1. 

Kid 3 has CDN and the other half of the area not asigned to kid 1.

Every kid has a third of the cake, a third of the frosted top and a third of the frosted sides. 

Edited on January 17, 2018, 11:28 am
  Posted by armando on 2018-01-17 11:01:13

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