I recently came across this puzzle:

There are 12 coins, all identical in appearance, and all identical in weight except for one, which is either heavier or lighter than the remaining 11 coins. Determine which is the counterfeit coin in only 3 weighings with a balance scale.

After struggling with this, both mentally and using pencil and paper, I decided to write a web page to simulate the problem; it can be found here. You may find it interesting to attempt this puzzle there before reading the discussion below. (more…)