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### Don't Fight over the Cake! (Weekly Brain Potion)

Don't Fight over the Cake! (Weekly Brain Potion)

This week we present our first Weekly Brain Potion, which will be a weekly brain teaser/mathematical puzzle posted each Friday. The problem is posted below, including a link to a discussion thread for the problem where everyone is encouraged to discuss the week's problem. Many of these problems will be adapted versions of common brain teasers, but try to avoid spoilers and solve them yourself! This week's problem:

Michael and his twin sister Michelle attend their friend's birthday party.

Being polite, Michael and Michelle let all the other guests get cake before taking their pieces. Unfortunately by the time they go to get cake, there is only one piece left!

The last piece of cake has some places with more frosting and some places with more sprinkles. Michael and Michelle want a fair way to divide the cake into two pieces for them to eat. They also have different preferences in what they want on their cake. Therefore cutting the piece evenly in half may not work! Each twin should think their piece of cake is at least as good as the piece the other gets.

Can you help Michael and Michelle decide how to divide the piece of cake?