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TROY by Ed Pegg Jr copyright (c) 1999

You and your opponent each have 12 plastic coins, and 12 small plastic weights.  The faces of your coins and of your opponents coins are distinctive, and come in 12 colors. (Aqua, Copper, Eggshell, Indigo, Lavender, Magenta, Neon, Orange, Pink, Silver, Tan, and Yellow -- PLASTIC MONEY). Each coin can hold up to two weights inside.  Once you snap the two halves of a coin together, only weighing will discern whether it is normal (one weight), lighter (no weight), or heavier (two weights).

Each person distributes all twelve weights among their coins.  The first person to sort out their opponent's coins wins the game.

Between the two players is a balance precise enough to weigh up to 12 coins. Each turn, a player may place up to six coins on each side of the balance. You will usually place your opponent's coins on the balance, but you can place some of your own coins on the balance as well.

Smaller games can be played.  For example, you could play with just nine coins.  Suppose your first five weighings are as follows: PCS > TEN, PAN > ICE, SAT > POE, COT = SIN, PIT = CAN.  How much can you determine about the nine coins?  Send Answer.

The number of possible combinations of n coins increases rapidly.  1, 3, 7, 19, 51, 141, 393, 1107, 3139, 8953, 25653, 73789.  This sequence is A002426 at the Encyclopedia of Integer Sequences.  It's the largest coefficient of (1+x+x^2 )^n.

From Luc Kumps --
There are 47 combinations left after the 5 weighings, and T canít be empty.

From Bob Harris --
I think if your were going to produce this game, you'd want to modify that rule slightly.  If I pick up my opponent's coins to weigh them, I may very
well be able to get a feel for how much each weighs while I hold it.  To prevent this, I think you'd want to make the rule be "Each turn, a player may DIRECT HIS OPPONENT to place up to six coins on each side of the balance."