Nine Coins
You have nine coins.
One of them is fake, and slightly lighter than the others.
How can you discover the fake, making only two measures with a balance?
Start by comparing three coins with three others.
If one pile is lighter, the fake is among those.
If measured piles have the same weight, the fake is in the pile you didn't weigh.
You now know which pile the fake is in.
Take two of those, and weigh them.
If one is lighter that is the fake, and if they weigh the same the fake is the one you didn't weigh.
You can use a similar method to discover the fake among
27 coins with three measurements,
81 coins with four measurements,
243 coins with five measurements,
729 coins with six measurements,
2187 coins with seven measurements,
6561 coins with eight measurements,
19,683 coins with nine measurements, and
59,049 coins with ten measurements.