12 Days of Christmas Gifts

A tradition, in our home, following in my mother's footsteps, is to have Pork Tourtiere for dinner on Christmas Eve.  For one of my sons this is the best dinner possible, and he has never understood why I don't make pork tourtiere throughout the rest of the year. (It wouldn't be as special then, would it?)

At 28, he has finally figured out a solution - he wants to make a minor modification to the 12 days of Christmas song:

On the first day of Christmas my mother gave to me, a very big delicious pork tourtiere.
On the second day of Christmas my mother gave to me, 2 pork tourtieres and a very big delicious pork tourtiere.
On the third day of Christmas my mother gave to me, 3 pork tourtieres, 2 pork tourtieres and a very big delicious pork tourtiere.

And so on.

So we decided to have some fun and do a bit of math to calculate how many gifts you would get (in his case, how many pork tourtieres) if you got all those gifts.  In my son's case, let's just say he would need a very large freezer and would have food for a year. Almost.

The sum is:
 1 +  (2 + 1) +  (3 + 2+ 1) + (4+ 3 + 2 + 1) + . . . + (12 + 11 + 10 + 9 +  . . . + 1)

I have shown the calculations on a separate document.  Take a minute to have a look!

Much to our surprise, the number of gifts you would receive, or the number of pork tourtieres my son would have, after the 12 days of Christmas, would be 364 - one less than the number of days in a year - one for every day EXCEPT Christmas day.  We liked that little coincidence.

And enjoyed a little recreational math along the way.

And needless to say, he's not getting all those dinners!