A good mind teaser for teenagers is "Johnny’s mother had three children. The first was named June, the second was July. What was the name of the third child?" The answer to this riddle is Johnny, as the question states that Johnny’s mother had three children and gives the names of the first two.
Another brain teaser appropriate for teenagers: "The manufacturer does not want to use it, the buyer does not need to use it and the user does not know he is using it. What is it?" The answer is a coffin. The manufacturer can be assumed to want to live as long as possible, so he does not want to use it, the buyer is alive, so he does not need it, and the user is dead, so he cannot know he is using it.
Good mind teasers can also take the form of a trick question. For example, "Before Mt Everest was discovered, what was the highest mountain in the world?" The answer is Mt Everest, as despite being unknown, the mountain does not cease to exist. The question is a trick in that it is worded in such a way as to lead the subject to believe that Mt Everest is excluded from the possible answers.