Mathematicians have long plagued humankind with a style of puzzle in which you must weigh a series of items on a balance scale to find one oddball item that weighs more or less than the others. They're known collectively as balance puzzles, and they can be maddening...until someone comes along and trots out the answer.
Within the world of balance puzzles, the 12-coin problem is well-known (there's also a nine-coin variant, and a horrendous 39-coin variant). There is in fact a generalized solution for such puzzles [PDF], though it involves serious math knowledge.
In the video below, we are presented with a version of the 12-coin problem in which we must determine a single counterfeit coin in a dozen candidates. The problem is, we're only allowed the use of a marker (to make notes on the coins) and three uses of a balance scale. Here are the detailed conditions:
1) All 12 coins look identical. 2) Eleven of the coins weigh exactly the same. The twelfth is very slightly heavier or lighter. 3) The only available weighing method is the balance scale. It can only tell you if both sides are equal, or if one side is heavier than the other. 4) You may use the scale no more than three times. 5) You may write things on the coins with your marker, and this will not change their weight. 6) There's no bribing the guards or any other trick.
So how do we solve this specific case? Watch the video to find out.
For a bit more on this puzzle, check out this TED-Ed page.