polya problem

[bekah24h]

Following recess the 1,000 students of a school lined up and entered the school as follows:
The first student opened all of the 1,000 lockers in the school
The second student closed all lockers with even numbers
The third student "changed" all lockers that were numbered with multiples of 3 by closing those that were open and opening those that were closed
The fourth student changed each locker whose number was a multiple of 4, and so on
After all 1,000 students had entered the building in this fashion, which lockers were left open?

 

[Deleted member 4993]

Following recess the 1,000 students of a school lined up and entered the school as follows:
The first student opened all of the 1,000 lockers in the school
The second student closed all lockers with even numbers
The third student "changed" all lockers that were numbered with multiples of 3 by closing those that were open and opening those that were closed
The fourth student changed each locker whose number was a multiple of 4, and so on
After all 1,000 students had entered the building in this fashion, which lockers were left open?

This problem involves "number of factors" of a natural number.

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