CAN YOU PLEASE HELP ME WITH THIS RIDDLE!?

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toonashley

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On international open a door day, 1000 neighbors line up at the beginning of their street (it is a long street). Each one of the doors on their street is aptly numbered 1 to 1000. The first neighbor opens all of the doors. The second neighbor closes every other door beginning with the second door. The third neighbor changes the status of every third door beginning with the third one (if opened, the neighbor closes it; if closed, the neighbor opens it). The fourth door changes the status of every fourth door. The fifth neighbor changes the status of every fifth door, and so on. Which door ust remain open after all 1000 neighbors have gone through all 1000 doors?


Explanation of answers PLEASEEEEEE
 
doors:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961
Are open

All perfect squares

Perfect squares have odd numbers of factors, because at the square root it's one number multiplied by itself;
eg:
1 has 1 factor (1)
2 has 2 factors (1,2)
3 has 2 factors (1,3)
4 has 3 factors (1,2,4)
5 has 2 factors (1,5)
6 has 4 factors (1,2,3,6)
7 has 2 factors (1,7)
8 has 4 factors (1,2,4,8)
9 has 3 factors (1,3,9)
Note that all perfect squares have an odd number of factors, others all have an even number of factors.
 
The first door i think?? Because if the 2nd person starts from the 2nd door and the 3rd person from the 3rd door and so on....then no-one else is going to shut the 1st door....unless im wrong and dont get this eiher, coz the answer seems too obvious.
 
1 cuz they started at 2


thats the simple answer

it seems too obvious i know, but most riddles are obvious!!!


xxxx
 
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