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People seem to like the brain teasers I’ve posted.  So here’s another.

I first ran across this when I was about 12 years old.  I still remember it as one of the toughest brain teasers I ever faced.

It is a very simple problem to explain, but the answer may not be obvious.  So take your time and think it through.

Find the Counterfeit Coin

You have 12 identical coins.  One of them is counterfeit.  The counterfeit coin may be heavier or lighter than the others.

Using a simple balance scale, and in just 3 weighings, identify the counterfeit coin, and determine whether it is lighter or heavier than the others.

The Challenge

Is it possible to solve this problem?

  1. If “Yes” then what is the solution?
  2. If “No” then why is it impossible?