Backcountry Notes

I woke up early one morning - - February 21, 2004, to be exact - - and, for no good reason at all, invented a game of solitaire while having coffee. I call it "Osama." Here is how it goes.

Cards: A standard 52-card poker/bridge deck, no jokers, well-shuffled.

Object:  To remove triplets of cards from a left-to-right layout so that only one card remains.

Rules: You are the Interrogator and you have in custody 52 suspects (in the form of the cards, of course). One of the suspects is Osama the Wily and Clever; he is well-disguised, but you are well-motivated to catch him, because there is a 25-million-drechma reward for his capture.

To interrogate the suspects, you deal them into a "lineup;" which is to say, you lay out cards in an overlapping line, left to right, beginning with four cards. Their stories “add up” and the suspects may be released when a combination of three cards adds to a total of 10, 20, or 30 points. Aces count as 1, face cards as 10. You may remove and discard, face-down, triplets of cards adding to 10, 20, or 30, by taking cards from either end or both ends of the lineup. Cards (suspects) thus discarded have been released from custody and may not be re-used during the game.

Example: For your initial lineup, you deal the following four cards: 7, 5, K, 5. You can remove and discard the 5, K, and 5, since they add to 20.

Another example: you deal 3, 7, 9, Q. You can remove 3, 7, and Q.

When you cannot remove a triplet, you turn another card face-up on the right-hand side of the lineup. Example: The layout is 3, 7, 9, 7; nothing can be removed; then you turn a 9 from the deck, yielding the following lineup: 3, 7, 9, 7, 9; still nothing can be removed; then you turn a King; the lineup is now 3, 7, 9, 7, 9, K; you can remove 3, 7 from the left, K from the right.

There is no limit to the number of triplets you may remove between turning new cards. For example, you have the lineup 3, 7, 8, Q, 9, J, 4, 2; the next card you turn is a King, making the lineup 3, 7, 8, Q, 9, J, 4, 2, K; you can now remove 3, 7 from the left, K from the right, leaving 8, Q, 9, J, 4, 2; next, you can remove 8, Q from the left, 2 from the right, leaving 9, J, 4. When a breakthrough comes in your interrogation, you may find that you can remove several triplets before turning another card.

Okay so far? Recall the basic idea: you are removing "suspects" in triplets; there are 17 triplets plus one extra card in a 52-card deck; so once you've removed 17 triplets, the remaining card is Osama, and you're 25 million drechmas richer.

More rules: you are not required to remove a triplet, even if it adds to 10, 20, or 30; you can leave it in the lineup for further interrogation, if you wish. Also, you may remove cards only from the ends of the lineup; no interior card can be removed. So if you miss a triplet, you have to leave it and get back to it later, if you can. Example: in the lineup 3, 6, 6, 8, K, K, 4, you cannot remove the triplet 6, 6, 8; you missed it, so it stays until you can remove the 3. Another example: in the lineup 5, 9, K, 7, 10, 1, you cannot remove the 9 in order to make a triplet with the 10, 1 on the right.

On the first run through the deck, you'll probably remove most, but not all, of the triplets. (It is possible to find Osama on the first run-through, but I estimate the odds against at around 400 or 500 to 1.) Although the triplets you have removed to the discard pile are gone from the game, those remaining in the lineup are still in custody; and, believe it or not, the odds are good that Osama is still among them. So simply reshuffle the remaining cards in the lineup and start again, dealing four cards, removing any triplet, and so on. Be careful, though; this is the point where Osama the Wily and Clever is most elusive, and even though you have him, he can easily slip through your grasp! If he escapes, you'll quickly reach the point where there are four or more cards remaining, but no possible triplets adding to 10, 20, or 30. Curses! You'll have to round up the suspects, reshuffle, and try again.

The chance of catching Osama seems to be about 40 to 45 per cent; however, you can more or less double your success rate if you learn Osama's own rules. Here's the catch: Osama's rules are secret; you have to figure them out for yourself!

Okay, okay, here's a hint: Osama's rules are inherent in the arithmetical properties of the standard 52-card deck of playing cards you are using. That's the only hint you're getting!