Student #3 then walks down the corridor and changed the status of all the lockers that are numbered with a multiple of 3. By the end of this scenario, 200 students will have walked down the corridor, in numerical order, with each student changing the status of those lockers that are numbered with a number that is a multiple of the student's number.
At that point, which of the lockers are open? More importantly, why are these lockers open?
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This is an interesting question.
(to help whoever actually comes up with the answer) I believe that the answer will involve the final students, using reverse logic.
For instance, the 200th student will toggle the 200th locker only, the 199th student will toggle the 199th locker only.
200-101 operate in this way.
The 100th student will toggle both the 100th locker and 200th locker.
The 99-67th students will operate in this way.
I'm not sure of how to deal with 1-66 with a method simpler than literally keeping track (not how this problem was meant to be solved) but the last 133 or so students are relatively easy to figure out toggling.
well, since some people shut lockers and some open them and some only toggle one .......