There are four types of common coins in   [https://en.wikipedia.org/wiki/United_States 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
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;Task:
How many ways are there to make change for a dollar using these common coins? &nbsp; &nbsp; (1 dollar = 100 cents).


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

(Note: &nbsp; the answer is larger than &nbsp; 2<sup>32</sup>).


;Reference:
* &nbsp; [http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-11.html#%_sec_Temp_52 an algorithm from MIT Press].
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