Scale Puzzles 301 - First Weighing: Left Side Down 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:    ^_(A+B+C+D)_/\_{_(E+F+G+H)_}
(the right side of the scale went down)

This told us that either

• The fake is lighter than a real coin and in the group (A+B+C+D), or
• The fake is heavier than a genuine coin and in the group (E+F+G+H).
• We also know that (J+K+L+M) are all genuine coins.

We created three new groups of coins by

• taking (B+C+D) off the left side of the scale (which includes the fake if scales balance second time)
• moving (F+G+H) from the right to the left side (which includes fake if scale tilts other way second time)
• moving (K+L+M) onto the right side of the scale
• The fourth group of three coins is (A+E+J), which did not move from their previous position. If the scale does not change its tilt, the fake coin is in this group.

What does this tell us?

Since the scale did not change its position, and still has the right side heavier, then the fake coin is one of the coins that did not change position. Either:

• the fake coin is (A), and it is lighter than a real coin, or
• the fake coin is (E), and it is heavier than a genuine coin.
• Remember, we know that (J) is Jenuine.

Third Weighing: Can you figure out a method to determine, with ONE use of the scales, which of the above statements is true. If you need more hints in order to develop your strategy, please review what we did in Scale Puzzles 102, when we had two coins, one of which was fake, and we had a third coin which we knew was genuine.

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.