Question: John has three daughters who are all unmarried. The youngest always lies, the oldest always tells the truth, and the one in the middle either tells the truth or lies. A very rich young man comes to John's house and says he wishes to marry one of his daughters. Naturally he wants to marry the oldest or the youngest so he will always know if she is lying or telling the truth. John agrees but says he can only ask one of the girls a yes or no question to decide which one he marries. They all look the same age.
What one question does he ask one of the daughters at random to figure out which daughter is the youngest or oldest?
Answer: "Is she older than her?" (He would ask one of the daughters if one of the other daughters is older than the last daughter). He always should pick the younger daughter based on what he knows. If he asks the older daughter and she says yes, then the youngest daughter will be known. If he asks the older daughter and she says no, then the youngest daughter is the other one. If he asks the youngest daughter and she says yes, she is lying and he will still pick the oldest. If he asks the youngest and she says no, he will just pick the other like in the first case. If he asks the middle daughter it doesn't matter because both will be acceptable choices.