Solve a Simpler Problem

Date: 09/25/2000 at 23:51:37
From: Marques Hunter
Subject: Solve a simpler problem

What day of the week is the 3,824th day after Wednesday? Where do I 
began to solve this?  How will figuring out problems like this help me 
in life?

Date: 09/26/2000 at 09:48:50
From: Doctor Rick
Subject: Re: Solve a simpler problem

Hi, Marques.

I doubt that you will ever need to know what day of the week the 
3,824th day after Wednesday falls on. Therefore I wouldn't bother 
memorizing the answer. It won't even be on the test.

The key is in your subject line: "Solve a simpler problem." That is a 
PROBLEM-SOLVING STRATEGY. You can forget the answer to this problem, 
and even the particular steps you followed, but if you remember the 
general strategy, you may well find that it will help you often. This 
is the purpose of problems like this: to help you learn strategies 
that will be useful for solving many problems you will encounter in 
the future (even if you think your job has nothing to do with math).

Take a cue from the subject line: think of a simpler but similar 
problem. How about this? "What day of the week is the 5th day after 
Wednesday?" This is so simple, you can just look on a calendar. 
Wednesday is the 27th; count 5 days, and you get to Oct. 2, a Monday.

I can guarantee you won't solve the original problem this way. You'd 
wear out your fingers counting that high. But try counting 26 days on 
the calendar. Do you notice that every time you count a multiple of 7, 
you're back on a Wednesday? The 7th day (Oct. 4), 14th day (Oct. 11), 
and the 21st day (Oct. 18) are all Wednesdays. 

Well, that makes sense: there are 7 days in a week. But how can you 
use this fact? After you reach the 21st day, you have how many days 
left to count? You were at a Wednesday, so what day is the 26th?

Now you have a method that can be generalized, so you can use the same 
method even for admittedly absurd numbers like 3,824. Can you state 
the generalized method? Can you use it to solve the original problem?

When you've done so, write down the answer and forget it. But remember 
the strategy you used to come up with the solution:

- Try a simpler problem of the same type as the original problem.

- If it's too simple, try a slightly harder problem, until you can see 
  a method for solving it that can be extended to handle the original 
  problem.

- State the generalized method.

- Use it to solve the original problem.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/