The Math of 'The 12 Days Of Christmas'

In the famous song "The Twelve Days of Christmas", how many gifts were given in total? See how Pascal's Triangle can be used to answer this question without mindless counting.

Twitter: @TPointMath

Image credits:

Twelve Days of Christmas: Xavier Romero-Frias
Snowman in front of tree: Digidreamgrafix

[wildreams]

It forms a tetrahedral? So it is scretly a Christmas Tree all along.

[BillRicker]

The math has always been more fun with this literal interpretation of the lyrics. This is a lovely presentation of it.

But i suspect the lyricist took grammatic liberty for benefit of scansion and means "gave" as "had given me so far", so that there's only 1 partridge and 5 gold rings total, only one kind of gift delivered each day.

(Note also that the 12 days of Xmas start on 12/25 and end on 3 Kings Day (1/6). The days before Xmas are Days of Advent, hence the calendars.)

[theInternet]

The formula for calculating the number of presents on the nth day is:
(1/6)*n^3+(1/2)*n^2+(1/3)*n
and i encourage you to prove this by manipulating the sigma representation of the items starting from k = 1 days up to n days.

[alandouglas]

New subscriber here... Love your work mate

[Gmackematix]

How many legs do all the gifts have at the end?

[benjaminbrewer]

Correct except that there are some days that there are hidden extra gifts. Each maid a milking has one cow. The geese a laying provide one egg each day. There’s a pair tree that comes with each partridge. Not to mention that there needs to be a body of water for a fairly large flock of swans a swimming.

[tylerclearwater]

(n)(n+1)(n+2)/6 where n is the number of days. :)

[mitsunam]

My teacher sent this video to our Basic Math class to watch it. 🥲 But your videos are really helpful!! 👍

[kellerr]

I'm sorry, but the correct answer is 376. The reason is because on the 1st day you actually receive 2 gifts. "A partridge in a pear tree". You receive the Partridge, and you receive the pear tree.