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Not sure how to divide the rent fairly? Simple. Use a triangle.

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Albert Sun and his friends moved into a small three-bedroom apartment where all the bedrooms were drastically different in size and other perks such as a nice view and natural lighting. They were challenged to figure out how to divide the rent up fairly based on what room each person got. Using the mathematical theorem called Sperner’s Lemma, Albert and his friends were able to come up with a fair solution. via New York Times:

The problem is that individuals evaluate a room differently. I care a lot about natural light, but not everyone does. Is it worth not having a closet? Or one might care more about the shape of the room, or its proximity to the bathroom.

A division of rent based on square feet or any fixed list of elements can’t take every individual preference into account. And negotiation without a method may lead to conflict and resentment.

I set out to find a better way to divide our rent. That’s how I came across a paper by Francis Su, a math professor at Harvey Mudd College in California, about a mathematical proposition discovered in 1928 by the German mathematician Emanuel Sperner. It is called Sperner’s lemma.

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