### How Many Legs You’d Get for Christmas

So, today I was at work, and the *Twelve Days of Christmas* became lodged in my brain for at least two hours, and I started to ask questions pertaining to the song, and it got a little bit strange. For example, considering the situation where you receive one of each present every day it appears in the song, how many birds would you get for Christmas in total. I’m not a mathematician, but I did my best.

First, you need to know all the birds in the song, and how many you get per round; that’s a partridge in a pair-tree, two-turtle doves, three-French-hens (we’ll assume these hens are chickens and not lobsters or Octopi), four-calling-birds, six-geese-a-laying, and seven-swans-a-swimming.

The partridge appears all 12 rounds,turtle-doves appear in the song eleven times, the French-hens ten times, the calling-birds nine times, the geese seven times, and the swans six times. But, we must also remember there are multiple birds, two-turtle doves, three hens, four calling-birds, six geese and seven swans. In one round of the final verse, including all the birds, you would have 34 feathered friends underneath one crowded Christmas tree.

So then I started to count backwards from 12 and added each load of birds from their respected rounds. Now, I am well aware this probably isn’t the fasted method of calculating the solution to this utterly redundant question, but as previously stated, I am no mathematician. From rounds 7-12 you would always receive 34 birds – 5 x 34 = 170. From 6-1 the arrival of birds would go as follows:

Day 6: 16 – 186

Day 5: 10 – 196

Day 4: 10 – 206

Day 3: 6 – 212

Day 2: 3 – 215

Day 1: 1 – 216.

And there’s the solution (I hope): According to the scenario that you would receive one of each gift every time it appears in the song, you would have 216 birds come the 6th of January.

**BUT THEN,** I pondered how many legs there would be in total under the same conditions. That is, if you receive one of each gift each time it appears in the song, how many legs would there be in total amongst your alarming multitude of gifts. The followed baffled its way through the labyrinth of my mind.

Okay, so … one partridge has 2 legs, two turtle-doves equal 4, three French-hens totals to 6, four calling birds is 8, rings have no legs thank Buddha, six geese max at 12 legs, seven swans would have 14, 8 maids-a-milking is complicated. The maids themselves would have 16 legs, but I assume, as should you, they are milking cows, which would add another 4 legs per cow, so 8 x 4 = (32 + 16) = 48. So, altogether eight-maids-a-milking would bring 48 legs to the table. Nine-ladies-dancing would carry another 18, ten Lords-a-leaping is 20 legs, eleven pipers-piping is 22, and 12 drummers drumming is 24. Breathe.

And so again, in the final verse all together: 2 + 4 + 6 + 8 + 12 + 14 + 48 + 18 + 20 + 22 + 24 = 178 legs.

Day 12 = 178

Day 11 = 178 – 24 = 154

Day 10 = 154 – 22 = 132

Day 9 = 132 – 20 = 102

Day 8 = 102 – 18 = 84

Day 7 = 84 – 48 = 36

Day 6 = 36 – 14 = 22

Day 5 = 2 + 4 + 6 + 8 = 20

Day 4 = 20

Day 3 = 20 – 8 = 12

Day 2 = 12 – 6 = 6

Day 1 = 6 – 4 = 2

So, we then add all the totals together to get the solution = 768 legs. If you were gifted one of each item on the list every time it appears in the song, you would be presented with 768 legs.

**BUT THEN – **In one round of the song what is the boy to girl ratio? Well, first we must discern the women from the men.

We don’t know the genders of the Partridge or the doves, but we are alerted to the fact that the French-hens are female by their description, and the geese are a-laying so we can factor them is as female also. From then on we only know the sexes of the human characters – the Maids-A-milking, and Ladies-Dancing are obviously women, while the Lords-a leaping are men. The instrumentalists are ambiguous with no specific notation to their genders. So again, in the last round of the song; 3 French hens, 6 geese, 8 maids-milking, and 9 dancing ladies = 26. However, again, the maids are milking cows, which must also be female, because they are able to produce milk adding an extra 8 girls to the pot – 26 + 8 = 34.

The men are easier since we only have the 10 lords-leaping to take into consideration, which is simply 10 gentleman per round.

Now, we have to work out the ratio – one of the few equations I actually remember from school.

Men: Women is 10:34 0r 1o/34

Now we cancel out a factor of six (or divide each number by 6) to bring the numbers down as low as possible –

10/6 = 1.6

34/6 = 5.6

Which means the boy:girl ratio is 2:6 (because we round-up to make the numbers whole, if I recall correctly, which I must say may be entirely incorrect). We can check by working backwards. First, we need to know the total of all the participants (if you can call them that) together = 10 + 34 = 44.

We know that for every 8 presents there are 2 men and 6 women. So now we need to know how many 8s go into 44.

44 / 8 = 5.5

We then multiply each number by this result – 2 x 5.5 = 11

– 6 x 5.5 = 33

To verify the answer we add the solutions together, and low and behold, 11 + 33 = 44 . So, the boy to girl ratio is correct at 2:6. For every 2 men sitting under your shambles of a Christmas tree, there are also 6 lovely ladies be they human, bird or large quadruped.

Okay brain, surely there can’t be anything else you want to kn- ** **

**HEY!** I wonder what the percentage of musicians in the last verse of the song is? … Oh yes, I’m not kidding. And thus …

So, I needed to add-up all the weird array of gifts in total first. Simple enough to calculate, because the song is about how many we get of each.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78. Of these there are 11 Pipers Piping and 12 Drummers Drumming, and 4 calling-birds. Now, I know the calling-birds actually refer to colly-birds, which are back-birds (which I will endeavor to explain later), but when I was little (well, littler anyway) I believed the birds were calling, as in singing, so I shall dub them musicians also.

The total number of instrumentalists = 11 + 12 + 4 = 27.

All I needed to do was find out what percentage 27 was of 78. Again, this is the easier mathy stuff I actually retained during high-school. All we need to is divide 27 by 78 and then times it by 100.

27 / 78 = 0.34 x 100 = 34.6 – which we round up to 35.

So the musicians make up 35% of the presents. Which, because I am terrible at this stuff normally, I will proceed to double check by working backwards. What is 35% of 78?

Well Radwell, 1% of 78 is 0.78, because all you do is divide a number by 100 to get 1%, thankfully. Therefore, 35% is 35 x 0.78 = 27.3 – rounded down to the nearest whole is 27.

**Mathematics win!** (I hope …)

Congratulations hypothetical audience, if you made it all the way through that muddle of words and numbers alive. If I got something wrong (which is a high possibility) let me now, so I can recalculate and update, because I refuse to let these questions of Christmas carol exploration go unsolved, or solved incorrectly.

From now on I’m going to stick to *Jingle-Bells *and *Deck the Halls. *They are less likely to seduce irrational questions, I’m sure.

January 25, 2011 at 00:23

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