Here’s a neat problem recently under discussion in our school district: “Four kids, each with their own lunch, go on a trip. When it’s time to eat, the four identical-looking lunches are mixed up and the kids randomly choose one. what is the probability that exactly one kid gets his own lunch?”
This problem is nice because it can be solved several ways, allowing students to see how others solve the problem. By relating the different methods of solution, students build and strengthen their own problem-solving abilities.
It’s also a nice problem because it reminds us that probability is a subject full of “slippery concepts”; just when you think you’ve solved a problem, it can elude you. Many probability problems are simple, but can be made more difficult by adding/changing just a few words in the posing of the problem. Consider how many high-level mathematicians were fooled by the Monty Hall problem, made famous by Marilyn vos Savant.
One of my KenKen posts asks the question, “How Many Possible Puzzles Are There?” This has resulted in many reader responses and a lively discussion. The question in today’s post may elicit many solutions as well – will one of them be yours?