Math Help?

[Holly]

Bwah, I need help, you high schoolers out there. This question is sort of like a practice question for the 7th grade Math Accelerated class, I guess, and I have no idea how to do it. I know there's a pattern, but I just can't put all of it together. >.<

Suppose an auditorium contains seats numbered from 1 to 1000 and there is a person sitting in each seat. They play the following game. The person in seat #1 instructs every person (including himself) to stand up. The person in seat #2 then instructs every other person (starting with himself) to sit down. The person in seat #3 instructs every third person (including himself) to change position (if they are standing, they will sit; if they are sitting, they will stand). This pattern continues through the person in the 1000th seat. How many people are left standing in the end?

^copied word for word^

Can anyone help, and know how you solved it?

[Hades]

I've never seen that one before, but I believe it's just that all the odd seats end up standing, and the evens are sitting. So isn't it just half of 1000= 500?

[Holly]

Nevermind, my dad's an effin' genius

It's 31. And it does have something to do with odds and evens.

[Hades]

Whoa, I read the question wrong. If it was the fourth kid, would they do every fourth person? I guess use permutations?

[Holly]

Yep, so every number with a factor of 4 would switch places.

[Ginger]

Brain hurts... xD

[Holly]

So the answer is basically the perfect squares between 1 and 1000.