Filling a Penny Album

Most coin collectors can trace their interest in the hobby back to that childhood day when they were given an empty coin album and encouraged to fill it up. This typically blue, typicallycardboard album contained slots the size of the lowest denomination coin in circulation (such as the U.S. one-cent piece or "penny"), with each slot labeled with the year in which that coin was minted. Fillingthe album requires collecting one coin of each mintage year. The first few days of owning an album are always marked by great success, with many slots quickly getting filled. As the days pass, progress gets slower and slower, as we keep getting repeated instances of previously collected years. The excitement builds as the number of slots gets whittled down one byone. Fillingin the last slot marks the satisfying end of a quest . Can we predict how many coins we will be expected to see before we complete an album? Determiningan answer requires modeling the process bywhich coins are removed from circulation and then solvingan interestingvariant of the famous coupon collector's problem. In this article, we tryto determine the number of U.S. pennies one must assay to construct a complete collection of Lincoln Memorial Cents. How Often Do I Get a 1959 Penny?