There are four types of common coins in   US   currency:

   quarters   (25 cents)
   dimes   (10 cents)
   nickels   (5 cents),   and 
   pennies   (1 cent) 


There are six ways to make change for 15 cents:

   A dime and a nickel 
   A dime and 5 pennies
   3 nickels
   2 nickels and 5 pennies
   A nickel and 10 pennies
   15 pennies


Task

How many ways are there to make change for a dollar using these common coins?     (1 dollar = 100 cents).



Optional

Less common are dollar coins (100 cents);   and very rare are half dollars (50 cents).   With the addition of these two coins, how many ways are there to make change for $1000?

(Note:   the answer is larger than   232).



References

 an algorithm from the book Structure and Interpretation of Computer Programs.
 an article in the algorithmist.
 Change-making problem on Wikipedia.


 
penny = 1
nickel = 1
dime = 1 
quarter = 1
count = 0
 
for penny = 0 to 100
    for nickel = 0 to 20
        for dime = 0 to 10
            for quarter = 0 to 4
                if (penny + nickel * 5 + dime * 10 + quarter * 25) = 100
                   see "" + penny + " pennies " + nickel + " nickels " + dime + " dimes " + quarter + " quarters" + nl
                   count = count + 1 
                ok
            next
        next
    next
next
see  count + " ways to make a dollar" + nl
 