Twelve Balls

You are given twelve balls. They are all equal in weight except for one that is either lighter or heavier than the rest. You are also given a balance. Using only three measurements, how can you find which ball is different and whether it is heavier or lighter?

Two Glasses

You have two glasses that are exactly the same size. One of the glasses has wine in it and the other glass has water. Both have the same amount of substance. You take a tablespoon of liquid from the glass with water and pour it into the wine. Then you take a tablespoon from the wine glass and pour it into the water. Which glass is more "polluted"?

Blue Eyes

A primitive group of natives lives on a remote island, lacking any modern technology. They are unusual in being exceptionally compassionate and intelligent. While most of the natives have brown eyes, they believe that having blue eyes condemns one to life a misfortune and misery. Whenever an islander is informed about having blue eyes, by custom the islander commits suicide in a lavish ceremony at midnight. Fortunately, there are no mirrors on the island. Islanders cannot see a reflection of their eyes. Furthermore, the islanders' compassion prevents them from informing the unfortunate. As a result, no islander has submitted to the morbid midnight ceremony. One day, a missionary visits the island. He is struck by the blue-eyed hara-kiri custom, but is too compassionate to inform the blue-eyed. On leaving the island, the missinoary announces: "I do not like your strange custom, but I respect your right to believe what you will. However, I feel compelled to tell you that at least one of you has blue eyes!" What happens next?