As a member of the Association of Coin Minters (ACM), you are fascinated by all kinds of coins and one of your hobbies involves collecting national currency from diff erent countries. Your friend, also an avid coin collector, has her heart set on some of your precious coins and has proposed to play a game that will allow the winner to acquire the loser's collection (or part thereof).
She begins by preparing two envelopes, each of them enclosing two coins that come from di fferent countries. Then she asks you to choose one of the two envelopes. You can see their contents before making your choice, and also decline the off er and take neither. This process is repeated for a total of r times. As the game progresses, you are also allowed to change your mind about your previous picks if you think you can do better. Eventually, your friend examines the envelopes in your fi nal selection, and from among them she picks a few envelopes herself. If her selection is non-empty and includes an even number of coins from every country (possibly zero), she wins and you must hand over your entire coin collection to her, which would make years of painstaking eff ort go to waste and force you to start afresh. But if you win, you get to keep the coins from all the envelopes you picked.
Despite the risks involved, the prospect of enlarging your collection is so appealing that you decide to take the challenge. You'd better make sure you win as many coins as possible.