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TROY by Ed Pegg Jr copyright (c) 1999
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 can’t 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."