Truth from a liar (Okay, this may be the only problem that you may argue the solution is not so rigorous.)
There is only one person on an island. He either always tells the truth or always lies, but you don’t know which is the case. You reach an intersection and don’t know if you should turn left or right.
You can only ask him one “Yes/No” question.
What question should you ask so you can figure out the direction you need to go?