Dear Economist,

Two friends and I have taken out a lease on a three-bedroom flat. The rooms are all different sizes. How should we decide who gets which room and the share of the rent that they should pay?

Daniel Chin, Haywards Heath, UK

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Dear Daniel,

This reminds me of the cake-cutting problem: one person cuts the cake, the other chooses which piece to eat. The person making the cut knows he will get the smallest piece and will try hard to make the pieces the same size.

With two rooms you can do the same thing. The first person decides on the size of the subsidy to the smaller room. For instance, for a £1,000-a-month flat, she might declare the small room costs £400 monthly and the large room costs £600. Her flatmate decides which deal she prefers.

With three rooms in a £1,000-a-month flat, things are more complicated. The first housemate fixes the rent on one room, say, £200 for the broom cupboard. The second housemate can take that offer or make the first housemate take it.

The third housemate then decides how the £800 should be split between the two remaining rooms and whoever did not get the first room decides which one to live in.

This scheme should be fair for the same reason as cake-cutting is fair: anybody who creates an unattractive option will immediately find himself having to take it.

Admittedly, if your housemates have different priorities it is an advantage to be the one making the divisions. For example, if your housemate needs a big room you can make sure it is expensive because you know he has to choose it. More sophisticated schemes can fix this problem but it may be better to make sure your housemates don't read this reply and simply go first yourself.

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