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.


100 PROGRAM "Coins.bas"
110 LET MONEY=100
120 LET COUNT=0
125 PRINT "Count  Pennies Nickles Dimes Quaters"
130 FOR QC=0 TO INT(MONEY/25)
150   FOR DC=0 TO INT((MONEY-QC*25)/10)
170     FOR NC=0 TO INT((MONEY-DC*10)/5)
190       FOR PC=0 TO MONEY-NC*5 STEP 5
200         LET S=PC+NC*5+DC*10+QC*25
210         IF S=MONEY THEN
220           LET COUNT=COUNT+1
230           PRINT COUNT,PC,NC,DC,QC
240         END IF
250       NEXT
260     NEXT
270   NEXT
280 NEXT
290 PRINT COUNT;"different combinations found."