Locker problem

Today our friends from across the hall came to join us and we worked in groups on solving a problem about lockers.

“There are 100 lockers, and 100 people. The first person walks by and opens all the lockers. Person 2 walks by and closes every 2nd locker (2,4,6,8…). Person 3 walks by and changes the state of each 3rd locker (if it’s open they close it, if it’s closed they open it). This continues until all 100 people have walked by. Which lockers remain open?”

Groups modelled the problem with many strategies: a drawing

a list

Some groups used smaller sets of lockers, and watched for patterns that could extend to the larger set.

It was lots of fun to see the different solution methods help groups arrive at an answer.

It was good to get our classes talking and interacting and solving together. Groups were explaining their thinking, and working hard justifying their conclusions to convince their peers.