Scale Puzzles 301: Second Weighing Balanced

Scale Puzzles 301 - Second Weighing: Balanced

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 found out that the scales balanced.

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

What does this tell you about the six coins that are on the scale?
What does this tell you about the six coins that are not on the scale?

What do the first two weighings tell you about eleven of the coins?
What do the first two weighings tell you about the only coin that has not yet been weighed?

Since (A+B+C) balances with (J+K+L), and because we already know that (A+B+C) are all genuine, we now know that (J+K+L) are also all genuine.

The fake coin must be one of the coins not on the scale.
The fake coin must also be one of the coins that was not on the scale during the first weighing.
Eleven coins have been weighed so far, only one coin was not weighed one time or the other.
That not-yet-weighed coin is your fake coin.

Third Weighing: You should now know which coin is the counterfeit. (Hint: the only coin that has not yet been weighed). Use your third weighing to figure out whether it is heavier or lighter than a genuine coin. If you still don't know what to do for your third weighing, reread the method for Scale Puzzles 102.

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.