I had to go back and look it up to make sure. So pay the first update no mind.
Most Helpful Guy
After quite some thinking i got it.
Here's what happens.
First, let's agree on the fact that prime numbers will be closed. Because the only factors they have are 1 and the number itself. So, if door opens at 1 , it has to close at the number itself.
Secondly, all other numbers will have factor , which can be grouped into pairs , for example take number 24, all possible factors are , 1,2,3,4,6,8,12,24 which can be grouped as , 1x24 , 2x12, 3x8, 4x6. If door opens at 1 it will go like
open close open close open close open close. It closes at the number itself.
But the exception lies in perfect squares where you have 5x5, 6x6 where u cannot account for 5 or 6 two times, therefore the door remains open.
1,4,9,16,25,36,49,64,81,100 will remain open.1
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