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.