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Cake Division Puzzle

  1. Oct 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Suppose that two people are dividing two cakes using the following rules:
    1. The first person divides the first cake into two pieces in any fashion.
    2. The second person then chooses which of the two cakes they will get to choose the first piece from.
    3. The first person then cuts the second cake into two pieces in any fashion.
    4. The second person chooses his piece of whichever cake he chose in step 2.
    5. The first person chooses his piece of the other cake.

    Devise a strategy that gives the first person as much cake as possible and say what that maximum amount is. Assume both cakes are the same size.
    3. The attempt at a solution

    The idea I think is multivariate calculus, seeing as that's what we are studying at the moment, but I also think this is just my prof being clever... I figured not cutting the cake at all would allow the first person a whole cake no matter what, but I'm not sure if that's allowed. Has anyone seen this before?
     
  2. jcsd
  3. Oct 14, 2010 #2
    Nobody has any idea?
     
  4. Oct 14, 2010 #3
    Suppose the first cake is divided in 2 pieces of size k and 1-k with k<=1/2

    If the second person chooses the first cake, he can get the largest piece of cake #1. He won't get anything of cake #2 because the first person can divide AND choose. So the second person ends up with (1-k)

    If the second person chooses cake #2 he can get the smallest piece of cake #1 and half of cake #2, so the second person gets (1/2)+k
     
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