Twelve Days of Christmas

12dayschristmastree

#1 How many total gifts are given just on day 10?
#2 How many total gifts are given during the twelve days?
#3 Suppose the song was changed to the “Nineteen Days of Christmas”? How many total gifts would my true love give to me?
#4 Generalize. How many gifts would be given on day n? How many total gifts would have been given on day n?

Here’s  a discussion of the relationship of the song to Pascal’s triangle.  The answers to #4 are C(n + 1, n – 1) and C(n + 2, 3).  [Note:  C(n+1, n-1) is translated as a  “combination of n+1 things taken n-1 at a time”.  Notation for combinations varies.]  Can you prove that the two answers given will always work?

Advertisements

Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s