Word Problem Hints

Date: 3/12/96 at 22:3:37
From: John Reichel
Subject: help

I have two questions I could use some help on.

1)  There are 1000 lockers numbered 1 - 1000.  Suppose you open 
all of the lockers, then close every other locker.  Then, for 
every third locker, you close each opened locker and open each 
closed locker.  You follow the same pattern for every fourth 
locker, every fifth locker, and so on up to every thousandth 
locker.  Which locker doors will be open when the process is 
complete?

2)  A certain substance doubles in volume every minute.  At 9:00 
a.m. a small amount is placed in a container and at 10:00 a.m. the 
container is just full.  At what time was the container on quarter 
full?

Could you please help me with these questions? I would greatly 
appreciate it.

John Reichel 

Date: 3/14/96 at 18:24:45
From: Doctor Jodi
Subject: Re: help

Hi John! 

Our office is overflowing with patients at the moment, so let me 
just try to put a bandaid on these problems for you... 

Thinking about the influence of FACTORS in the first problem might 
help.

I imagine the row of lockers as a long line of off/on switches.

Let me give you a hint on the second question.  If the substance 
doubles every minute, when was the container half full?  Can you 
use the same sort of approach to find out when it was a quarter 
full?

I hope these ideas help you a bit; please write back and let us 
know how the problems are going, or to ask for more help when you 
need it.

-Doctor Jodi,  The Math Forum