12 Coin Hint

12 Coin Hint


Here's a helpful hint to the 12 coin problem: If I balance 3 coins on both sides, say 1-3 against 4-6, and I find that the balance tips one way, then I remove one from each side, say 1 and 4, then I swap two, say 2 and 5, then if the balance tips the same way, I know it's 3 or 6; if the balance tips the other way, I know it's 2 or 5; and if the balance is equal, then I know it 1 or 4. I also know what way the scale tipped the first time, so isolating it down to two, I only have to measure one of the remaining two against a known good coin to determine if it's that coin or the other, and if it's even on that last measurement, the first measurement tells me the orientation of the other coin.
Give up already? Here's the solution.
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