Ways to Make 50 cents

Date: 8/29/96 at 19:52:59
From: Richard M Crea
Subject: Ways to Make 50c

Dear Dr. Math,

How many ways can you make 50 cents? We came up with 50 ways. How 
close are we?

Thanks for your time,

Tina

Date: 8/30/96 at 16:15:43
From: Doctor Alain
Subject: Re: Ways to Make 50c

To solve this kind of problem, it is important to sort the different 
ways you find properly. I live in Canada, where we have a 50 cent 
coin. I'm not sure if you have one, but this is the way I would do it.


Part 1  How many ways can I make 50c using a single 50c coin (that's 
        easy).

Part 2  How many ways can I make 50c using no 50c coin (that's 
        harder).

Part 2.1 How many ways can I make 50c using no 50c coin and 2 
         quarters.

Part 2.2 How many ways can I make 50c using no 50c coin and 1 quarter.

Part 2.2.1 How many ways can I make 50c using no 50c coin and 1 
           quarter and 2 dimes.

Part 2.2.2 How many ways can I make 50c using no 50c coin and 1 
           quarter and a single dime.
...etc...

Part 2.2.3 How many ways can I make 50c using no 50c coin and no 
           quarter and no dime.
...etc...

Part 2.3 How many ways can I make 50c using no 50c coin and no 
quarters.
...etc...

Then you just add the answers found in the different parts. 

I also get 50 ways.

-Doctor Alain,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/