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.


c = 0
for p       = 0 to 100
  for n     = 0 to 20
    for d   = 0 to 10
      for q = 0 to 4
       if p + n * 5 + d * 10 + q * 25 = 100 then
         print p;" pennies ";n;" nickels "; d;" dimes ";q;" quarters"
         c = c + 1
       endif
      next q
    next d
  next n
next p
print c;" ways to make a buck"