Summer SAVY 2019: Session 1, Day 3 – Puzzles and Problem Solving (Rising 5th/6th)
Most of the morning in Puzzles and Problem Solving was spent converting our classroom into an airplane…or at least a room with 7 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 two turns as the nice person at the back of the line and the “not-so-nice” person at the front of the line. When asked before the activity what the answer to the question was, most students said 1 out of 7. Then we acted out the problem, and the last person got his or her seat in 6 out of 14 trials! One thing that might be fun would be for you to try out a miniature version of this problem at home.
The actual probability is 50%, and, somewhat surprisingly, it doesn’t matter how many people and seats are on the airplane, as long as the number of seats is equal to the number of people in line. 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.
Shortly before lunch, I introduced the dreaded “Polar Bears and Fish” riddle. I was very impressed that the students were able to figure this one out today. It was great to see how they recognized patterns and started to develop a sense for the problem, even when they didn’t really understand what the riddle was trying to get them to see.
We spent a fair amount of the afternoon investigating Sudoku puzzles and learning some tricks and strategies for completing them. Students then worked both individually and in small groups talking about puzzles of varying difficulty. I also look forward to challenging them with more interesting Sudoku puzzles later in the week.
We wrapped up with the “Three Hats” puzzle, a logic riddle about determining the color of one’s hat. While we solved the problem today, we also laid the groundwork for acting out the problem over the course of the next two days. In “our version,” the final participant, the one who can’t see anyone’s hats, is the winner, but it is possible to arrange the hats so that any of the three win.
It’s hard to believe that class is more than half over! I am so excited to see what these students come up with over the course of the last two days!