There’s those initial investments we make when we first move in: a garbage can, laundry detergent, an industrial-sized package of red cups. But what if Joey has a meal plan, and won’t use any of the cooking oil? And what if Audrey bought her own special shampoo and isn’t sharing with everyone else? Or there’s prude Eric, who won’t pitch in for whipped cream. People get picky about what they will and won’t pay for — multiply that by four roommates, and it can get tricky to split the bill.

Here’s how to settle all you roommate debts as fairly as possible without a charlie foxtrot. The basic idea is a simple chart that will break down each charge to account for: who initially paid for it and who’s splitting the bill. Once you’re finished, money will only exchange hands a few times with almost no change to deal with. Last night, we settled about \$400 worth of really small items in about fifteen minutes — but you can do it with rent, utilities, party supplies — anything.

1. Gather your roommates, the receipts, a calculator and piece of paper. A spreadsheet is only going to make things more confusing, so just do it by hand.
2. Create the magic square. This thing is a lot like one of those logic puzzles from fourth grade. Each person’s name appears once in a column and a row. The columns signify who paid for the bill and the rows signify how much money that person owes to the bill in question. Leave plenty of space to do math in the middle. You can go ahead and put crosses through the boxes that correspond to people and themselves. It’s much easier to not pay yourself back…
3.

4. Go through each receipt or bill, item-by-item. For each item, decide who’s going to getting in on it and split the price accordingly. For instance, I bought a huge thing of disgusting boxed wine. Kelly is an alcoholic, so he drank about 90% of it. We split it 9 to 1 and we just listed “9″ in Kelly’s box under the column for my bills — since I paid for it (and I don’t need to pay myself back), nothing goes in my box. Since you’ll probably split most things four ways, keep a tally of those things on a piece of scratch paper to the side, total them at the end of the bill, split them four ways and list the amounts in each person’s box.
5. Total the boxes and cancel shit out. This is the cool part. Look at the boxes for, say, Nelson and Scarlett — there’s one where Nelson owes Scarlett money and another where Scarlett owes Nelson money. You can cancel these values to simplify the payments. See who owes what to whom and list those numbers out separately.
6. Be logical and make the payments. Now, you can use the transitive property to cancel out even more on paper. For instance, if Bobby owes Cheryl \$8 and Cheryl owes Katka \$8, Bobby can just pay 8\$ to Katka. There are other more complicated simplifications, but don’t spend too much time on it. Divvy out the money.

Taxes are something we didn’t factor in. Instead, we rounded all the change up to help account for that a bit.

I think it’s also interesting to see how “screwed” people could have gotten if you hadn’t split everything up. In the end, you might find that it wasn’t worth the whole process for one person to get reimbursed for only \$10.

I was looking for a program that would easily do this sort of thing. Any tips?