# Re: the 97% rule and american education standards (LONG)

Gordon Irlam (gordoni@base.com)
Sat, 6 Apr 1996 18:44:35 -0800 (PST)

> > If, in a school of 1,000 lockers, one student opens every locker, a second
> > student closes every other locker (second, fourth, sixth, etc.), a third
> > student changes every third locker (opens closed lockers and closes open
> > lockers) and so on until the 1,000th student changes the 1,000th locker,
> > which lockers are open? <bg- huh? I don't even know where to begin without
> > doing it longhand and taking an entire day>
>
> This is a little nasty, isn't it, folks? Frankly, it's even beyond SAT work
> (which I had a 13 something on that year).
>
> Let's see: student n changed every nth bit. So, locker k is changed by #of
> divisors. And they want you to compute the PARITY of the number of divisors of
> every number from 1-1000? Well, we know all the prime lockers are closed, so
> we can use the prime density as an upper bound... :-)
>
> Nutso. I mean, they tried this on Math Team, but for *everyone*? They're
> kidding themselves.

Hmmm, parity?? Rohit? Grade 8 math?

1, 4, 9, 16, 25, ...

Factors come in pairs
Except when squares...