Mrs. Jones was very proud of her apple tree. One autumn, after harvesting her apples, she called her three sons together. "Here are 150 apples," she said. "I want you to take them to the market tomorrow and sell them for me." She gave Paul 15 apples, Nick 50, and Ben 85. "Your job," added Mrs. Jones, "is to sell the apples in such a way that each of you brings home the same amount of money." How do they do it?
There are three crates, one with apples, one with oranges, and one with both apples and oranges mixed. Each crate is closed and labeled with one of three labels: Apples, Oranges, or Apples and Oranges. The label maker broke and labeled all of the crates incorrectly. How could you pick just one fruit from one crate to figure out what’s in each crate?
There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?