The plane problem is a real-world problem, presented without any suggestion as to how it might be solved. It arose unexpectedly as the author was messing around on the internet, not thinking about maths at all. She did not encounter the problem in a maths lesson, nor as homework in the middle of a unit on a particular topic, and so she had no clues about what method was going to be useful, or even if she would be able to solve it. All she had--initially at least--was the image of the plane and a mystery: at what altitude is it flying? There is something satisfying about seeing how mathematics can solve a mystery that may appear, at first sight, to be intractable. Students need the opportunity to attempt such problems, and to see no only that mathematics offers powerful tools for solving problems, but that the very process of learning to problem-solve is worthwhile as well.