An algebraic riddle ... the king has an ongoing deal for anyone in the kingdom. He has 9 coins, one of them is lighter than the rest. However, you are not allowed to touch the coins to weigh them. The king gives you a two pan balance. If you figure out the fake coin in one try you get the kingdom, in 2 tries you'll be second in command, in 3 tries you'll be sent to jail, four or more you'll die. How do you find the fake coin?

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