I have also used this with the perms and combs unit and linked in Pascal's Triangle. The song playing in the background is always a nice change that time of year.
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Ok my math teacher gave use this problem but yes i understand the logic but aren't we over thinking Christmas?!? Ok, that is the answer counting each item as a separate gift, but are 12 Drummers Drumming 12 separate gifts, or just 1 gift of 12 Drummers? In which case the answer is Last night a friend asked me if there was an equation to figure out the number of presents in the 12 days of Christmas, and this is what I came up with:. For me the puzzle began on a long drive home from college for Christmas break many many! I ended up graphing the result in three dimensions.
In the end, this formula turned out to be the answer, where x is the number of days:. James - Your formula does give , but only works for 12 days. If we do the number of presents up to 3 days, it's a non-integer result.
How Many Birds Are In The 12 Days Of Christmas Carol?
Dean - Thanks for the story! A little bit of algebra shows your formula to be the same as mine - so it is correct! Actually there is a fundamental flaw in this, misunderstood by many and unfortunately spread by the masses at the festive season in the form of a 'fun puzzle' The answer is quite simply 78 As humans we look for patterns and we try to over complicated already simple things. Firstly there are 12 days, a comon misconception is that the answer gives you a present a day excluding Christmas Day. This is not so, the clue is in the name. Secondly, the meaning behind the song is biblical and religious.
It's actually blasphemous to suggest that there are more than indicated in the song. For example A partridge in a pear tree is actually Jesus. For Christians, you cannot possibly count him 12 times. I must congratulate you on your excellent method and working out though, it's very well structured and had this problem been worded differently would be completely valid. Well, no, I think that Charlotte is technically correct, and the singer did actually receive only 78 gifts.
The repetition is poetic, not legally accurate. But that's over-thinking it. The math problem is based on "what if?
The Twelve Days of Christmas (song) - Wikipedia
It's an interesting sequence, even though it would seem to be one that doesn't often come up in ordinary life hence my inability to find it in my math textbook. Getting the solution was work, but it was fun.
I agree: the pear tree should be counted as a separate gift. So should the geese eggs, the pool for the swans, the cows or goats for the maids, the drums for the drummers and the pipes for the pipers. James' formula is intuitive and correct. And for a value of 3, the formula does not come up with a non-integer result, nor could it. There is no integer value for d you can choose that would produce a non-integer result, as the formula is comprised of exclusively operations of addition in one form or another - both multiplication and subtraction are various forms of directly increasing or decreasing quantities, or, addition in a negative or positive quantitative direction.
And since no division is involved, no non-whole or imaginary number could be produced by plugging in only whole numbers. So, unless my true love decides to give me a bonus gift of perhaps two-thirds of a calling bird, on say, the two-and-one-quarterth day of Christmas, only whole numbers of days and gifts will result. Plugging 3 into James' formula for the number of days will result in 10, the correct answer. You say "So, how many presents are there altogether?
The Twelve Days of Christmas (song)
Making all gifts in total would take a lot of time, and even just making the 78 gifts of the last verse will be a […]. She said it was based on an arithmetic progression.
I couldn't see how now I can , but realised the answers to 1x12, 2x11, 3x10, What was the AP though? Turned out to be a quadratic sequence, with a 2nd diff of Working out the rest, we get 13n zero term is 0. Merry Christmas from Great Yarmouth College. And of course besides triangle and tetrahedral numbers, squares may be invoked also. Thus for 12 days of Christmas we merely have six simple squares to add. Well my young nephew, posing this old chestnut found in a Christmas cracker, thought such addition easier than grappling with the formula.
There is an ever quicker way to calculate the answer. Instead of making 12 calculations and then adding all the answers, just do the first six and then double their total. Additionally, it seems that the maids a-milking must have had a cow or some other lactating animal to milk and therefore there would be 40 cows animals bieng milked and proffered as gifts along with the maids a-milking. Your blog URL can be left blank. Notify me of followup comments via e-mail. Your comment:. Preview comment. Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates twice a month.
Join thousands of satisfied students, teachers and parents! From Math Blogs. By Murray Bourne , 16 Dec A partridge in a pear tree. Resource - real life math topics 2. Thanksgiving for less math? The true cost of the 12 days of Christmas There is an index that tracks the total cost of the items in the song New names for the days of the week Perhaps it's time to move away from the ancient names used for the days of Christmas costs and the true meaning Some thoughts on Christmas , including what we really should spend our money on Merry Christmas Living in Singapore, you get a different view on religious "holy days".
Each of the "days" represents some aspect of the Christian Faith that was important for children to learn. However, many have questioned the historical accuracy of this origin of the song The Twelve Days of Christmas. While some have tried to debunk this as an "urban myth" out of personal agendas, others have tried to deal with this account of the song's origin in the name of historical accuracy see Snopes on The 12 Days of Christmas.
There is little "hard" evidence available either way.
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Some church historians affirm this account as basically accurate, while others point out apparent historical and logical discrepancies. The reality is that the "evidence" for both perspectives is mostly in logical deduction and probabilities. Lack of positive evidence does not automatically provide negative evidence.
On the other hand, logical deduction and probability do not provide proof either. One internet site devoted to debunking hoaxes and legends says that, "there is no substantive evidence to demonstrate that the song 'The Twelve Days of Christmas' was created or used as a secret means of preserving tenets of the Catholic faith, or that this claim is anything but a fanciful modern day speculation.
The view of the song as a secret catechism is most likely legendary or anecdotal.
Without corroboration and in the absence of "substantive evidence," we probably should not take overly rigid positions from either perspective. It is all too easy to turn the song into a crusade for personal opinions. That would do more to violate the spirit of Christmas than the song is worth. So, for the sake of historical accuracy, we need to acknowledge the likelihood that the song had secular origins.
However, on another level, this should not prevent us from using the song in celebration of Christmas. Many of the symbols of Christianity were not originally religious, including even the present date of Christmas, but were appropriated from contemporary culture by the Christian Faith as vehicles of worship and proclamation. Perhaps, when all is said and done, historical accuracy, as important as that might be on one level, is not really the point.
Perhaps more important is that Christians can celebrate their rich heritage, and God's grace, through one more avenue during the Advent and Christmas seasons. After all, is that not the meaning of Christmas anyway? O n the 1st day of Christmas my true love sent to me In the song, Christ is symbolically presented as a mother partridge that feigns injury to decoy predators from her helpless nestlings, much in memory of the expression of Christ's sadness over the fate of Jerusalem: "Jerusalem! How often would I have sheltered you under my wings, as a hen does her chicks, but you would not have it so.
O n the 2nd day of Christmas my true love sent to me Two Turtle Doves The Old and New Testaments, which together bear witness to God's self-revelation in history and the creation of a people to tell the Story of God to the world. O n the 3rd day of Christmas my true love sent to me O n the 4th day of Christmas my true love sent to me Earlier English versions have "colley birds" or blackbirds. There are other versions as well. O n the 5th day of Christmas my true love sent to me O n the 6th day of Christmas my true love sent to me O n the 7th day of Christmas my true love sent to me O n the 8th day of Christmas my true love sent to me Matthew O n the 9th day of Christmas my true love sent to me Nine Ladies Dancing The nine Fruit of the Holy Spirit: 1 love, 2 joy, 3 peace, 4 patience, 5 kindness, 6 generosity, 7 faithfulness, 8 gentleness, and 9 self-control.
Galatians O n the 10th day of Christmas my true love sent to me Ten Lords A-leaping The ten commandments: 1 You shall have no other gods before me; 2 Do not make an idol; 3 Do not take God's name in vain; 4 Remember the Sabbath Day; 5 Honor your father and mother; 6 Do not murder; 7 Do not commit adultery; 8 Do not steal; 9 Do not bear false witness; 10 Do not covet. Exodus O n the 11th day of Christmas my true love sent to me Luke The list does not include the twelfth disciple, Judas Iscariot who betrayed Jesus to the religious leaders and the Romans.
Related The 12 Days Of Christmas: A Carol and Count Book
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