In the introduction of the book “Thinking Mathematically” by
Mason, Burton and Stacey, you can read: “Probably the single most important lesson
to be learned is that being stuck is an honourable state and an essential part
of improving thinking”. This phrase gave me the courage to share my approach to solving this locker problem.
As I have
learned to code in the past, the first impulse was to try to find an algorithm
that would help me find the answer. I couldn’t find any, and I decided not
to look for AI solutions or suggestions. I left the problem for the next day. The next day I scribbled my reasoning on a paper and didn’t have luck. I started to
listen to some classmates talking about the problem, and I avoided them. I
wanted to think about the solution by myself.
Finally,
I decided to solve the problem manually. I went into Excel and started simulating
row by row the action of each student. I coloured the cell yellow if the cell
represented a closed locker, and I left the cell without any fill if the locker
was open. After the 4th student, I could deduce a pattern, but I kept
the simulation until student #49.
My conclusion
was that the lockers that will be closed are:
1 2, 22, 32, and so on until
312, which corresponds to locker 961. The rest of the lockers will
be open.
During the exercise, I found myself playing to find patterns
of distance between numbers, and the beauty of the figure formed by the yellow
colour. (See image 2)
I still don’t know how to express the solution in a
mathematical expression, but I had a lot of fun playing with my model and
sharing it with my family.
No comments:
Post a Comment