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How Many Gifts Are in the 12 Days of Christmas?

How many gifts should one's true love be given on each of the 12 Days of Christmas? If you stick to recommendations from the classic song, the answer can be calculated using some clever math. Keep on reading to find out how.

By
Jason Marshall, PhD,
December 23, 2016
Episode #296

Page 1 of 2

Partridge In a Pear TreeOnce upon a time, in a far away land, a young girl and boy were playing in the dining room of their castle when they discovered a story scrawled on the back of a painting. As legend has it, the story read …

So Christmas was weird for me last year. It all started on December 25 when my true love gave me a potted pear tree upon whose branches sat a befuddled bird. Things got even weirder the following day when I received yet another pear tree (complete with yet another bird), as well as a pair of doves. The story on the third day was similar—another pear tree, two more doves, and this time a trio of chickens. As you might imagine, I was wondering: What’s up with all the birds?

This sort of thing continued for more than another week. With each new day came a new gift—actually a predictable number of that new gift: 3 on the 3rd day, 4 on the 4th, 5 on the 5th, and so on—as well as a repeat of all the gifts given on all of the previous days. By the time we got to the 12th day, we ran out of space in the castle living room and had to move our holiday celebration to the very dining room in which this painting is hanging.

That evening as we sat around the table, somebody asked me how many presents my true love had given on each day? With that question we began a quest to understand the mathematics of those epic twelve days of Christmas. To the best of my recollection, dear reader, the following contains an accurate recounting of that tale of discovery.

The Wonderful (and Distracting) World of Puzzles

As so often happens, our journey towards counting my true love’s gifts was quickly derailed by another math puzzle. Somebody at the table mentioned that someday far into the future (in the year 2016), psychologist and magician Richard Wiseman (who was once a guest on the famous “Math Dude” show) would tweet the following series of instructions (which you should feel free to follow along with … you might want to go grab a calculator):

  • Type your house number (i.e., your address) into a calculator.
  • Now double it.
  • Next add 5 to the result.
  • Then multiply this answer by 50.
  • Now add your age.
  • And then add 365 to the result.
  • Finally, subtract 615 from the whole thing.

What do you get? As Wiseman points out: “Voila—your house number and age!” Needless to say, all of us at the table gave it a go, and much to our amazement we found that it does indeed work (so long as you’re less than 100 years old). Upon realizing this, roars of curiosity erupted: “Why? Huh? How can this be? I MUST KNOW NOW!”

So, exactly how does this puzzle from the future work? Good question, dear reader.

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