Scale Puzzles 301: Second Weighing, left side went down

Scale Puzzles 301 - Second Weighing: Left Side down

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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)_

Second Weighing: You decided to weigh A+B+C (which the first weighing told you were genuine) on the left and J+K+L (one of which MIGHT be fake) on the right, and the left side of the scales went down.

_{_(A+B+C)_}/\^_(J+K+L)_

What does this tell you about (J+K+L)?

Since the first weighing told us that (A+B+C) are genuine, then (J+K+L) must include the fake coin.

We still don't know which one, J, K or L, is the counterfeit coin, but we now know that the fake is either heavier or lighter than a genuine coin. Just look at the image again:

_{_(A+B+C)_}/\^_(J+K+L)_

Is the counterfeit coin heavier than, or lighter than, a genuine coin.

Third Weighing: You should now know that the fake coin is (_heavier or ^lighter) than a genuine coin. (Hint, heavy goes down, light goes up). Use your third weighing to figure out whether J, K or L is the fake coin. I'm not going to tell you the method, but you can figure it out by going back and reviewing the method I used in Scale Puzzles 101.

You are now done with this set of possible results.

Click here to return to the Scale Puzzles 301 Top Page and try another set of possible results.

There are nine different "third weighing" pages, like this one, that you can eventually reach.