Children’s cereal manufacturers often attract the attention of young clients by including small prizes and toys in every box; sometimes all prizes are identical, but most often individual prizes are part of a collection, and kids are encouraged to collect them and try to complete a full collection. How long does it take ?
Simple probabilistic modeling shows that on average \(n (1 + 1/2 + \ldots + 1/n)\) boxes are required to complete a full set of \(n\) prizes: for example, it takes on average \(14.7\) boxes to complete a full set of six prizes.