The cake is a lie! pt. 2

Probability Level 4

Suppose a group of n n people want to split a group of whole cakes among each other. Each cake is of one type only e.g. vanilla, chocolate, strawberry, etc.

Is it possible to divide the cakes among all n n people such that each person receives greater than a total value of 1 n \frac{1}{n} ?

If you are confused, see this problem .

Problem source: AMST 2015 Power #1c. Image source .
It depends on the value functions It depends on the number of people Always possible It depends on something else not listed here Never possible It depends on the size of the cakes

Steven Yuan by Steven Yuan , 20, USA

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1 solution

Jonathan Yang
Mar 1, 2015

It exists iff not all players have the same value function.

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