Things you'll never need to know how to do

Two brainteasers, one easy and one not so much. The easy one is: Start with the numbers 5, 5, 5, and 1. Using any of the four basic operators, get the result of 24.

The more interesting one: You have twelve indistinguishable objects and a two sided balance. Eleven of them way exactly the same amount, one of them is either heavier or lighter than the other eleven. Given three weighs, explain how to determine which of the twelve it is, and whether it's heavier or lighter.

I'm sure the answers to both of these are googleable, but that wouldn't be much fun now, would it?