How many calling birds

All 12 things it professes to secretly represent—the books of the Bible, the six days of creation, etc. For another thing, this rumor seems to have popped up in the last 25 years, and then spread like wildfire, as such things do, on the interwebs, without reference to any original sources.

But scholars on the subject and yes, there are scholars on the subject! There were however, for some reason, always four of them. Another rather credible origin story concerns the partridge himself. Over the years, the song has been done and re-done by everyone from the Chipmunks, Winnie the Pooh "a hunny pot inna hollow tree! In some retellings, the game worked a little more like Spin the Bottle: if a kid messed up, he owed someone a kiss the musical version of mistletoe!

There was one chocolate on the first row, then 3 on the next, then 6, then 10 etc. Assuming the tower is solidly filled with the chocolates, the total number of chocolates in this tower is T 17 , the 17 th tetrahedral number, which works out to be chocolates — just what you need if you have lots of family visiting over the Festive Period.

Now I just have to figure out what to do with all those Partidges in all those Pear Trees. Merry Christmas to all! Last Name. These partial sums are called tetrahedral numbers , because they can be drawn as 3-dimensional triangular pyramids tetrahedrons like this:. Of course, we could just start adding with our calculator, but what if my true love is very generous, and starts giving me presents for 30 days after Christmas?

Or for days? How would I calculate it then? Our aim is to produce a formula that will allow us to find any tetrahedral number. Here's one of the possible ways of doing this. Let's take for example the sum of the first 4 triangular numbers and represent it as a triangle. Each row in the triangle on the left, below adds to a triangular number and the sum of the whole triangle is the sum of the first 4 triangular numbers.

Let's now re-arrange the first triangle in 2 different ways, then add the result, in respective positions. My total is 3 times what I really need. I will divide by 3 later to cater for this.

Notice that by doing this, I get a total of 6 in every position in the result triangle. The answer of "6" is 2 more than the 4 triangular numbers that we are adding. The formula for the sum to n terms of an arithmetic progression with first term a and common difference d is:.

Dividing this by 3 since we used 3 equivalent sum triangles to get this far gives us the n -th tetrahedral number:. If my true love gave me the presents in this pattern for 30 days, I would have this number of presents:.

See the 66 Comments below. Posted in Mathematics category - 16 Dec [ Permalink ]. This is incredible. But first I will have to send it by my husband to show me all the ins and outs of it.

Thanks for doing it. Thanks for your post. I believe that students shouldn't take a break from thinking just because school is out! This is a perfect way to keep those brains working while integrating it with something most people will be doing anyway-so why not just slip a math problem in the stocking next to the mp3 player?

Great idea! Awesome, i encountered this problem in haven of all places and i came up with the long way of figuring it out no-one told me it but a friend of mine used the method above or something similar , she told me if you picture it, it forms like a triangle and i just thought to myself i'm not even going there i was bewildered but fascinated but since then i have been looking at different maths problems as the whole magic of maths has got to me lol. This is so wonderful I have linked it to christianity, Jesus had 12 apostles and in 12 days gifts are given which is almost the number of days in a year.

Dont you think all this is the work of God? That is why I believe that mathematicians are blessed by God. Well, I love the advanced maths, but not the basic counting error. The Twelfth Day of Christmas is of course the 5th. Count them. The Epiphany is the following day. Hi Fill. According to this article , "[The Epiphany] falls on 6 January or, in many countries, on the Sunday that falls between 2 January and 8 January.

Isn't there a flaw in this? On the 1st day of Christmas, my true love gave to me a partridge in a pear tree. Sorry but that is TWO gifts. This is so wonderful and is perfectly acknowledged. Triangular numbers [ Or any student. But before you go clicking that link, take [ Myra - Yes, after I wrote it, I also wondered if it was quite right. I think I meant to say "The pear tree was not a separate gift.