100 Doors Puzzle Or Door Toggling Puzzle

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Question: This is a very common interview puzzle. The problem is very simple if you understand it. So the point to note is, do not arrive at the solution so "fast”, if you are asked this puzzle in an interview and if you are not planning to show any acquaintance with this puzzle. Problem goes like this : There are N doors in a row numbered from 1 to N. Initially all are closed. Then you make N passes by the N doors. In pass 1 you toggle the all the doors (1,2,3,4....)starting from the first door. In the second pass you toggle every second door(2,4,6,8,...). In the third pass you toggle all third doors(3,6,9...).Similarly you make N passes. Question is what is the state of door k after N passes. This is a simple but requires clear mathematical Logic. Normally asked version has N=100. Solution: CLICK HERE POST YOUR OPINION IF YOU HAVE BETTER SOLUTION

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Question:
This is a very common interview puzzle. The problem is very simple if you understand it. So the point to note is, do not arrive at the solution so "fast”, if you are asked this puzzle in an interview and if you are not planning to show any acquaintance with this puzzle.

Problem goes like this :
There are N doors in a row numbered from 1 to N. Initially all are closed.
Then you make N passes by the N doors. In pass 1 you toggle the all the doors (1,2,3,4....)starting from the first door. In the second pass you toggle every second door(2,4,6,8,...). In the third pass you toggle all third doors(3,6,9...).Similarly you make N passes.

Question is what is the state of door k after N passes.
This is a simple but requires clear mathematical Logic.
Normally asked version has N=100.

Solution:
CLICK HERE

POST YOUR OPINION IF YOU HAVE BETTER SOLUTION