Scale Puzzles 301 - First Weighing: Balanced Back to Top of Puzzle * * Please help us keep our puzzles free! * * Back to <www.MAZES.com>

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You have twelve coins (A, B, C, D, E, F, G, H, J, K, L & M). One of the coins is counterfeit, but you don't know if it is heavier or lighter than the others. You are allowed to use a balancing scale three times to find the counterfeit. Find a strategy that will allow you to find the counterfeit in three weighings, no matter which one is fake.

First Weighing: You decided to weigh (A+B+C+D) on the left and (E+F+G+H) on the right, and found out that the scales balanced.

_(A+B+C+D)_/\_(E+F+G+H)_

What does this tell you about the eight coins on the scale?
What does this tell you about the four coins that aren't on the scale?

The balanced scale tells us that all eight coins on the scale are genuine. This means that the fake coin is not on the scale (J+K+L+M). You don't know if the fake is heavier or lighter than a genuine coin.

Since we know that the first eight coins are genuine, let's use that to our advantage. Let's weigh three genuine coins against three from the other group and see what happens.

Second Weighing: Put A+B+C on the left. Put J+K+L on the right Compare: A+B+C ^ J+K+L	There are three possible outcomes: The sides balance, A+B+C = J+K+L Left side goes down, J+K+L are lighter Right side goes down, J+K+L are heavier
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