A magazine subscription service deals with 35 magazines. A subscriber may order any number of them. The subscription service is trying to computerize its billing procedure and wishes to assign a different computer key (identification number) to two different people unless they subscribe to exactly the same magazines. How much storage is required; that is, how many different code numbers are needed?

There can be \(2^{35}\) different subsets (subscriptions) of 35 magazines, assuming we allow subscribers with 0 subscriptions. If not, then \(2^{35}-1\) is enough.