The Twelve Days of Christmas is one of the most popular Christmas carols, telling of a zealous suitor’s extravagant Christmas gifts to his sweetheart. The familiar words of the carol were published in London, around the year 1780, in a collection of children’s rhymes called Mirth without Mischief. It was included in this context as a memory game with accompanying forfeits for the forgetful.
The Twelve Days of Christmas is the source of much amusement among mathematicians in that it provides the basis for a suitably festive mathematical brainteaser, that of ‘How many gifts does the young lady, who narrates the carol, receive?’
Looking at the lyrics closely it soon becomes apparent that on day two his sweetheart receives two turtle doves and another partridge. On the third day of Christmas she gets the French hens, another pair of turtle doves and yet another partridge, pear tree, the works. And so it goes on...
There is actually a mathematical formula you can use to work out the total number of gifts given by the extravagant ‘my true love’ celebrated in The Twelve Days of Christmas on any one day of the twelve days. Where N is a particular day out of the twelve, the total number of gifts given on that day = N(N+1)(N+2)/6.
So, rather than receiving a total of 78 gifts over the twelve days, the narrator of the carol actually receives 364 individual items, one for each day of a traditional year, minus Christmas Day.
You can find out more about why we give presents each Christmas inside Christmas Explained: Robins, Kings and Brussel Sprouts, which would itself make the perfect present for your loved ones this Christmas.
* And if they don't, then they probably deserve a present for being so virtuous!
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