When Roommates Figure Out How to Split the Rent

Seven years ago, when two of my friends and I were out of grad school and getting a jumpstart on our careers, we decided we wanted to find a three-bedroom apartment in the city for as cheap as we could possibly find it in a relatively safe neighborhood that wasn’t terribly far away from public transportation. After some looking, we landed in Woodside, Queens and found a three-bedroom for $1,800. There was one small room that could fit a full bed, dresser, and a small desk. There was a normal size room that could fit those items easily, and the third was the largest—a “master” with its own bathroom.

I volunteered for the smallest bedroom with the sole intention of paying the least amount of rent, while my two other friends took the other rooms. Then it came to dividing the rent.

“How should we do this?” I asked. “My room is probably half the size of yours and doesn’t have a bathroom.”

We threw out some numbers and decided on, I believe, the very first set we put out: I would pay $550, the roommate with the second larger bedroom would pay $600, and the roommate with the master would pay $650.

“I’m fine with that,” I said, and so were the others.

In retrospect, I probably should have paid even less, but $550 for a bedroom in New York City seemed like such a steal at the time—just right before the financial crisis—that I thought more about how it would allow me to save a normal amount of money and go out to dinners and for drinks on a regular basis. Plus, we all liked each other and got along, and it was an ideal living situation except the place desperately needed updating.

In the Times, Albert Sun looks at a mathematical way we could have decided on who would pay what for rent, and it’s called “Sperner’s Lemma” and has to do with triangles:

You’ll have to go to the Times to add more triangles and play around with it, but I doubt my roommates would have actually have gone through the trouble of using this particular algorithm, even if we had known about it at the time. We paid our respective rents for the next two years and none of us ever had a complaint.

Photo: Dan Deluca

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