How many ways are there to make change for a dollar using nickles, dimes, quarters, and half dollars?


11 – nickles and dimes, 0-10 dimes
17 – quarters, nickles and dimes, 8+6+3
11 – half dollars, 1+1+3+6

39 <== finally. i’ll get it, really i will. ;-)

the way to think about it is,
with only nickles and dimes, you can have 0, 1, 2, … 8, 10 dimes and the rest nickles

with quarters, you can have 4 or 3 or 2 or 1. if you have 3, then you can have 0, 1, 2 dimes. if you have 2 quarters, you can have 0, 1, 2, 3, 4, 5 dimes (and the rest nickles).

One thought on “How many ways are there to make change for a dollar using nickles, dimes, quarters, and half dollars?

  1. 11 – nickles and dimes, 0-10 dimes
    17 – quarters, nickles and dimes, 8+6+3
    11 – half dollars, 1+1+3+6

    39 <== finally. i’ll get it, really i will. ;-)

    the way to think about it is,
    with only nickles and dimes, you can have 0, 1, 2, … 8, 10 dimes and the rest nickles

    with quarters, you can have 4 or 3 or 2 or 1. if you have 3, then you can have 0, 1, 2 dimes. if you have 2 quarters, you can have 0, 1, 2, 3, 4, 5 dimes (and the rest nickles).
    References :

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>