Let *X*[*n*]= *T*[*n*] - *T*[*n*-1] where *T*[*n*] is the number of medallions collected when you *first* own *n* *different* medallions. Hence *X*[1]=1, but what do we know about *X*[*n*] for other values of *n*?

It might also help to remember, if *X* and *Y* are random variables, the average (or *expectation*) of *X* + *Y* is the same as the expectation of *X* + the expectation of *Y*. In symbols we may write this as

Have fun!

We will publish the best explanation in the next issue, along with the answer to the problem itself.