Math/Algebra Problem

[demenion]

Need help with this problem from School

At Dunbar Highschool, there are 500 lockers, numbered 1 through 500. Suppose the first student opens each locker. Then the second student closes every second locker. The third student changes the state of every third locker (that is, closes the ones that were open and opens the ones that were closed). The fourth student changes the state of every fourth locker. this process continues until the 500th student changes the state of the 500th locker. Which lockers are left open at the end?

 

[StageLeft]

I'm so glad I'm done school so I don't have to work my mind with things like this

 

[Killbat]

It develops an exponential pattern. Figure out the first few and you'll see.

...
Or just write a program to brute force the solution. (like my friend)

 

[Regine]

The perfect squares will be open, the rest will be closed. For all non-perfect squares, there are an even number of factors (i.e. 24- 1,2,3,4,6,8,12,24)- there must be an even number of factors, as they're all pairs. However, with the perfect squares, one "pair" of factors is a single number- (i.e. 5 and 5 for 25). So perfect squares are the only ones that can have an odd number of factors.

 

[axelfox]

69

 

[GoldenBear]

Wow tool girl, you're smart.

Let's get married.

 

[Mucman]

I had that exact question as a bonus question on a grade 11 exam... I got it right , looks like Toolgirl knows what's going on.

 

[Napalm381]

First, I wrote the solution, I just posted it under her name. And as for "let's get married"...you wish. She'd never marry a boy-band listening loser like you

 

[Bling Bling]

wow, she's got good taste in music, is blonde, and has a nice set of br--ains. *sigh*

edit: whoa....."she" turns out to be a grey bull....well i'll be damned...

 

[ManSnake]

Oh, I have lived in Ames, it is a fine city if you know what I am saying

 

[Napalm381]

<< wow, she's got good taste in music, is blonde, and has a nice set of br--ains.
whoa.....&quot;she&quot; turns out to be a grey bull....well i'll be damned... >>

Don't worry, all of the nice things you said about her still apply. Rest assured she and I are not the same person

 

[Bling Bling]

Napalm: i really do hope you aren't the same...actually it would be a lot more interesting if you were the same...i think the forum had one such person a while back before i actually joined. Nowhereman or something like that. and i'm babbling again.

Ames: that's twice you've said it today (or maybe it was a day or two ago)...me thinks something fishy is going on...


Bling Bling = confused s.o.b.

 

[Napalm381]

<< i really do hope you aren't the same >>

Don't worry, we aren't. As if I could flirt like she does


<< i think the forum had one such person a while back before i actually joined. >>

ChipBGT/Thunderbooty/Hyper99 was always amusing

And yes, we do live in Ames, IA.

 

[Bling Bling]

i was there for chip. he (she? ) rocked. always good to have someone else from ol' GA.

I figured out you two live in Ames, IA, but why does Mansnake keep saying &quot;Oh i have lived in Ames, it is a fine city if you know what i am saying &quot;

I love off-the-wall comments. That's what i'm all about. I'm a retard.

 

[Mister T]

dememion....

The answer is 22 lockers. Toolgirl's method is correct