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If you have reached this page by following a link from another
web page or from a search engine, please click here
to start at the Scales Puzzle 301 first page.
This web page is one of the "second pages" to "Scale
Puzzles 301" (part of the Scale Puzzles Puzzle
Series at <www.MAZES.com>. If you reached
this page with a link from another web site, please ask that webmaster to
change their link to one of the starting pages listed here.
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 right 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 (lighter or heavier) than a genuine coin. (Hint, light goes up, heavy goes down). 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.