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Imagine there are 2 cakes and you are the second person to choose a piece. Since person 1 is sure to claim the biggest cake, you have the choice to either pick the smaller cake or half of the bigger cake.
Behind you is your friend who also wants some cake, assuming you chose to split the larger cake, then your friend can either claim the smaller cake or split the bigger cake with the 3 of you
So this seems like a greedy algorithm,
edit: I guess I didn't explain the last step. Once you optimize for the solution where not everyone recieves the same volume as an intermediate step, you can find the volume everyone gets by dividing each volume by how many people and returning the minimum.
- rzhng April 17, 2013