What’s the most annoying Christmas song? Even “Last Christmas” must lose with the old English carol “The Twelve Days of Christmas”.
It’s a cumulative song, which means that each verse adds something to the previous one. It starts quite innocently:
On the first day of Christmas my true love sent to me
A partridge in a pear tree.
(Partridge is a bird and no, there’s nothing wrong with you if you have no idea what it looks like.) The next verse goes like this:
On the second day of Christmas my true love sent to me
Two turtle doves,
And a partridge in a pear tree.
Then we sing:
On the third day of Christmas my true love sent to me
Three French hens,
Two turtle doves,
And a partridge in a pear tree.
Only the strongest will survive until the last, twelfth verse, to announce to the world:
On the twelfth day of Christmas my true love gave to me
Twelve drummers drumming,
Eleven pipers piping,
Ten lords a leaping,
Nine ladies dancing,
Eight maids a milking,
Seven swans a swimming,
Six geese a laying,
Five gold rings,
Four calling birds,
Three French hens,
Two turtle doves
And a partridge in a pear tree.
Apart from some questionable gifts (I mean, sending someone ‘eight maids a milking’ doesn’t sound legal), this song contains a lot of maths. How many gifts did my true love give to me in total?
A partridge in a pear tree appears in each verse, which means I received it 12 times in total. Two turtle doves appeared at my doorstep 11 times, three French hens 10 times etc. Finally, I got only one set (set?!?!?!) of twelve drummers drumming, in the very last verse. In total, I received
gifts in total. Before you take out your calculator, notice that the first and last items in this sum are the same. This also holds for the 2nd and 11th, 3rd and 10th, 4th and 9th, 5th and 8th, as well as 6th and 7th, which means we just need to calculate
That’s quite a few gifts, almost one for each day of the year! In fact, we just computed the twelfth tetrahedral number, for which one can find a general formula. I bet this song was written by a mathematician!
Oh, and my true love, please don’t send me any geese. Thank you.
Certain about Uncertainty 