Home > A Level, Maths, Resources, Teaching > A nice little number puzzle

## A nice little number puzzle

Today I shared this puzzle with my further maths class. I was amazed how quickly they got it, and they asked if they could do another. One of them said “Google ‘Hard maths puzzles'”, so we did and found this nice website which I think warrants more exploration.

The puzzle we selected to discuss was:

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

The discussion around it was very interesting and I thought worth sharing here.

I tried to take a back seat during the discussion, which went a little like this:

Student A: “There’s at least 1 – The first person will open the first locker and no-one else will touch it.”

Student B: “Likewise, locker 2 will be shut. And 3”

Student A: “4 will be open!” then while inking “5 shut, 6 shut, 7 shut, 8 sht, 9, open” then “Will all the square numbers be open?”

Student C: “Yes! they will!”

Me: “Why?”

Student A: “They have an odd number of Factors!”

Me: “Indeed, but the question asks for how many…”

Student C: “the square root of 1000 is 10 root 10”

Student A: “That’s around 10pi”

Me: “So?”

Student A: “That’s 31 point something so there are 31 open because the next square will be 32!” (That’s an exclamation, not a factorial)

Me: “Excellent”

Categories: A Level, Maths, Resources, Teaching
1. May 8, 2014 at 2:01 pm

Reblogged this on The Echo Chamber.

2. May 8, 2014 at 10:45 pm

Totally lovede this, especially your class’s persistence in riddling it through and not looking for a facile formula.

3. May 8, 2014 at 10:48 pm

Loved. Can’t type.