Sunday, September 15, 2024

My Process of the Locker Problem

After reading through the problem, I started using excel to map out the status of every locker after each student took their turns (0 being closed, 1 being opened). In my work, I started with 0 for all lockers, which are all closed. After I reached 10, I indicated all of the lockers which had their status changed from Closed to Open. The ones which was changed at the end was 1, 4, 9 which happened to be perfect square numbers.

I suspected it has to do with the total number of divisible factors being odd number for perfect squares. Then I expanded this exercise to 16, and it turns out my theory was correct. For example, a non-perfect numbers like 12 has six (even) divisible values: 1, 2, 3, 4, 6, 12. On the other hand, a perfect number like 16 has five (odd) divisible values: 1, 2, 4, 8, 16. This theory also applies to prime number which always have two divisible values: 1 and itself.

In conclusion, the number of open lockers is the total count of perfect square values under 1,000.



at

2 comments:

  1. MaliheSeptember 21, 2024 at 1:43 PM

    Hi Raymond, I got a bit confused by your explanation and the Excel sheet. In the first row of your sheet, you marked all the lockers as closed, but in the second row (which indicates the first student’s turn), you show all the lockers being opened. However, the question states that the first student closed all the lockers. Could you clarify this part for me? Thanks!

    ReplyDelete
    Replies
    1. Raymond YeOctober 9, 2024 at 7:13 PM

      Hi Malihe, I see that now. However, it does not affect the solution as initially closed locker and be interchanged with initially open locker.

      Delete

Subscribe to: Post Comments (Atom)

My Final Reflection on EDCP 342

Here we are, the end of the road of EDCP 324. Although it was only around 3.5 months, this was the most I have thought about Math as a subje...