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mgf1107lecture7

# mgf1107lecture7 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 7 The Divider-Chooser Method Consider two people sharing a cake. How can it be divided so that both people get their fair share? The divider-chooser method involves one person cutting the cake into two pieces of equal value, and the other choosing which piece they want. This simple method may seem like the end of the story with regards to dividing a cake, but we have to consider what will happen if the cake os not uniform, and the preferences of the players are not the same. Ex. Damian and Cleo go to the county fair. In a raffle they win a cake that is half chocolate-half strawberry. Damian likes both flavors equally, while Cleo does not like chocolate. How do they divide the cake? Note: It is always better to be the chooser, since the divider will never get more than 50% of their total valuation.

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Ex. Jared and Karla buy a 12 inch sub for \$8 that is half vegetarian (inches 0-6) and half meatball (inches 6-12). Jared prefers meatballs three times as much as vegetables, whereas Karla (though Jared doesn’t
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mgf1107lecture7 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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