In reply to DaveHK:
> The total number of presents the subject of the song receives is 364. A partridge in a pear tree for 12 days, 2 turtle doves for 11 days etc etc.
> To the Maths literate on the forum (and I know there are a few), does this illustrate any deeper rules in Maths or is it just a novelty? Is there for example, a simple way of working out the total of such series?
The number of presents each day are triangular numbers: 1, 1+2=3, 1+2+3=6 etc. so the total number is the sum of the first 12 triangular numbers: 1+3+6+10+15+21+28+36+45+55+66+78=364
The general formula for the sum of the first n triangular numbers is n(n+1)(n+2)/6
This is a bit technical but standard stuff to prove, but you can check that putting n=12 gives (12x13x14)/6=364
Anyway, if Christmas had n days, the total number of presents would be n(n+1)(n+2)/6
So if Christmas lasts all year (not far from the truth!), there should be (365x366x367)/6=8171255 presents.
EDIT: Some simple algebra shows that my formula is equivalent to keiths's (though I've no idea how he got it from a spread sheet!)
Post edited at 21:45