Why were there 12 days? Why not 13 or 15? What is the significance of 12 days?
Obviously I am not the first to wonder about this as there are a number of sites dealing with this very issue. Most of these sites agree that the 12 days have a significance in the Christian calendar and that each of the gifts are Christian symbols.
I am more interested in the numerical value chosen. The 12 days after Christmas to Ephiphany are meaningul in the church calendar. But that doesn't explain why they became the 12 days before Christmas in the song.
It turns out that 12 is an "abundant" number in mathematics. That means if you add 12 to the sum of its other divisors, 1,2,3,4 and 6, the result is more than 2 X 12.
I can picture an early mathematician creating the "12 days of Christmas" song to teach his math students more about abundance using the first abundant number, 12, as his starting point.
Now you've got something really interesting to talk about over that next glass of eggnog.