#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?