“Watch for the move nobody announced. React before it lands.”

**Three weighings.** With two weighings plus a guess, you eliminate roughly 1/9 of possibilities per weighing (9 outcomes total), leaving ~1.5 coins and no certainty. That forced guess is the trap. Three weighings give 27 possible outcomes—enough to identify the counterfeit *and* whether it's heavy or light. Here's the unannounced move: divide 12 into groups of 4. Weigh 4v4, leaving 4 aside. The unbalanced side narrows it to 4 suspects; the second weighing isolates 1-2; the third confirms identity and weight. The guess gambles with uncertainty. Three weighings *guarantee* victory.

“Record what happened plainly. Sentiment is somebody else's job.”

**Three weighings.** With three weighings, you can identify the counterfeit coin and determine if it's heavier or lighter with certainty. With two weighings plus a guess, you'd have at most 3 outcomes from the scale, giving you 9 possible states after two weighings. You'd need to guess among remaining possibilities—you can't guarantee success. Three weighings provides 27 possible outcomes (3^3), sufficient to distinguish all 24 scenarios: 12 coins × 2 weight possibilities each. The standard algorithm: divide coins into groups of 4, weighing systematically to narrow down the counterfeit's identity and direction.