The cake is a lie! pt. 2

Discrete Mathematics Level 4

Suppose a group of \(n\) 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 \(n\) people such that each person receives greater than a total value of \(\frac{1}{n}\)?

If you are confused, see this problem.

Problem source: AMST 2015 Power #1c. Image source.

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