The Ultimate Word Problem. Part One.

I know of a word problem which is, in my opinion, The Ultimate.
In order to tell it, I have to give an easier one first, just so the other will make sense.
Here's how it goes:

Suppose you had nine coins. Eight of them gold and one counterfeit. The eight gold coins are the same. The counterfeit one is almost perfect. The only way to tell the difference is by weight.
Now suppose you had a balance. The kind with a tray on either side such that if you place something on each side, the heavier side will go down and the lighter side will go up. Suppose the tray is large enough to hold as many coins as you need to place in them.
Finding the counterfeit coin becomes an easy task. Simply begin by placing a coin in each tray and if they are the same, the two trays will remain level. Then substitute another coin in one of the trays until you find which one is different.
But suppose you wanted to do it in the fewest measurements possible. It can be done in three measurements.
So the problem is: How can you determine in three measurements 1)which coin is counterfeit 2) whether the counterfeit is heavier or lighter than the real ones

Hint: Start by placing three coins in each tray.


Coming next....part two, the hardest word problem you have ever seen in your life