Summer SAVY 2016 (Session 1, Day 3) – Puzzles and Problem Solving
Most of the morning in Puzzles and Problem Solving was spent converting our classroom into an airplane…or at least a room with 16 seats and boarding passes. Consider the following scenario: The first person to board a fully-booked flight drops his or her boarding pass and doesn’t bother to pick it up. The person doesn’t know where to sit and therefore just takes any seat he or she likes.
Everyone else boards the plane and takes his or her assigned seat if it is available. If it is not available, the passenger also takes any available seat he or she likes in the airplane. The question we investigated was, “What is the probability that the last person to board the plane gets to sit in his or her assigned seat?”
Each student got to take a turn as the nice person in the back of the line and the “not-so-nice” person in the front of the line. When asked before the activity what the answer to the question was, most students said something beneath ten percent. Then we acted out the problem, and the last person got his or her seat in 9 out of 16 trials!
The actual probability is 50%, and, somewhat surprisingly, it doesn’t matter how many people and seats are on the airplane. We will spend more time later in the week discussing the basics of this “Airplane Math.” Our discussion today was mostly conceptual, but we will delve into the calculations that justify this counter-intuitive answer.
We also spent a fair amount of the afternoon investigating Sudoku puzzles and learning some tricks and strategies for completing them. Several students asked to bring some extra puzzles home, so I think it was a fun afternoon! I do look forward to challenging them with more interesting Sudoku puzzles later in the week!
Also this afternoon we investigated a logic problem where a person is able to determine the color of the hat he is wearing just from information obtained earlier in the problem. It was fun to act this out with the students as well. We modeled our black and white hats with construction paper, and students took turns playing different roles in the scenario.
It’s hard to believe that class is more than half over!