12 Days Of Xmas Help ME! (Very Long Post)

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Can someone please help me.

We all the know the song "The Twelve Days of Christmas"

Now assuming on each day, the singer receives what he sings on each day, how many gifts will he have ended up with by the twelfth day?

I have done a couple of things (Yes, it is a very slow day in here today, come on half five)

First thing I did was this :

A rundown of each gift, and how many of each was reveived.

1 partridge in a pear tree received on each of 12 days
12 x 1 = 12
2 Turtle Doves received on each of eleven days
11 x 2 = 22
3 French Hens received on each of ten days
10 x 3 = 30
4 calling birds received on each of nine days
9 x 4 = 36
5 gold rings received on each of eight days
8 x 5 = 40
6 geese a laying received on each of seven days
7 x 6 = 42
7 swans a swimming on each of six days
6 x 7 = 42
8 maids a milking received on each of five days
5 x 8 = 40
9 ladies dancing received on each of four days
4 x 9 = 36
10 lords a leaping received on each of three days
3 x 10 = 30
11 pipers piping received on each of two days
2 x 11 = 22
12 drummers drumming received once
1 x 12 = 12

So here we have it (12 + 22 + 30 + 36 + 40 + 42) x 2 = 364

The second thing I did was this :

On the First Day he receives One Partridge in a Pear Tree.
Amount of Gifts Received Day 1 = 1
What he has already plus what he received today
0 +1 = 1

On the Second Day he receives One Partridge in a Pear Tree, Two Turtle
Doves.
Amount of Gifts Received Day 2 = 3
What he has already plus what he received today
1 + 3 = 4

On the Third Day he receives One Partridge in a Pear Tree, Two Turtle Doves,
Three French Hens
Amount of Gifts Received Day 3 = 6
What he has already plus what he received today
4 +6 = 10

On the Fourth Day he receives One Partridge in a Pear Tree, Two Turtle
Doves, Three French Hens, Four Calling Birds
Amount of Gifts Received Day 4 = 10
What he has already plus what he received today
10 + 10 = 20

On the Fifth Day he receives One Partridge in a Pear Tree, Two Turtle Doves,
Three French Hens, Four Calling Birds, Five Gold Rings
Amount of Gifts Received Day 5 = 15
What he has already plus what he received today
20 + 15 = 35

On the Sixth Day he receives One Partridge in a Pear Tree, Two Turtle Doves,
Three French Hens, Four Calling Birds, Five Gold Rings, Six Geese-a-Laying
Amount of Gifts Received Day 6 = 21
What he has already plus what he received today
35 + 21 = 56

On the Seventh Day he receives One Partridge in a Pear Tree, Two Turtle
Doves, Three French Hens, Four Calling Birds, Five Gold Rings, Six
Geese-a-Laying, Seven Swans-a-Swimming
Amount of Gifts Received Day 7 = 28
What he has already plus what he received today
56 + 28 = 84

On the Eight Day he receives One Partridge in a Pear Tree, Two Turtle Doves,
Three French Hens, Four Calling Birds, Five Gold Rings, Six Geese-a-Laying,
Seven Swans-a-Swimming, Eight Maids-a-Milking
Amount of Gifts Received Day 8 = 36
What he has already plus what he received today
84 + 36 = 120

On the Ninth Day he receives One Partridge in a Pear Tree, Two Turtle Doves,
Three French Hens, Four Calling Birds, Five Gold Rings, Six Geese-a-Laying,
Seven Swans-a-Swimming, Eight Maids-a-Milking. Nine Ladies Dancing
Amount of Gifts Received Day 9 = 37
What he has already plus what he received today
120 + 37 = 157

On the Tenth Day he receives One Partridge in a Pear Tree, Two Turtle Doves,
Three French Hens, Four Calling Birds, Five Gold Rings, Six Geese-a-Laying,
Seven Swans-a-Swimming, Eight Maids-a-Milking, Nine Ladies Dancing, Ten
Lords-a-Leaping
Amount of Gifts Received Day 10 = 47
What he has already plus what he received today
157 + 47 = 204

On the Eleventh Day he receives One Partridge in a Pear Tree, Two Turtle
Doves, Three French Hens, Four Calling Birds, Five Gold Rings, Six
Geese-a-Laying, Seven Swans-a-Swimming, Eight Maids-a-Milking, Nine Ladies
Dancing, Ten Lords-a-Leaping, Eleven Pipers Piping
Amount of Gifts Received Day 11 = 58
What he has already plus what he received today
204 + 58 = 262

On the Twelfth Day he receives One Partridge in a Pear Tree, Two Turtle Doves,
Three French Hens, Four Calling Birds, Five Gold Rings, Six Geese-a-Laying,
Seven Swans-a-Swimming, Eight Maids-a-Milking, Nine Ladies Dancing, Ten
Lords-a-Leaping, Eleven Pipers Piping, Twelve Drummers Drumming
Amount of Gifts Received Day 12 = 59
What he has already plus what he received today
262 + 59 = 321

The Total here is 321

Question is, why do the two totals not match, and what am I doing wrong?

Fudger

Your life must be very sad indeed............

seamus

I'm sure there's a mathematical way of expressing what you get - "12!" or somesuch.

Slow day yeah?

At the start - why multiply it by two?

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Fudger wrote:

Your life must be very sad indeed............

Charter

Charter wrote:

What is not allowed is as follows

Flaming
- Posts containing personal attacks on another user will be edited/deleted.

Did you really feel the need to post what you posted?

I am asking a legitimate question, and showing why I asked it.

seamus wrote:

At the start - why multiply it by two?

Because the same sum is done twice, the same numbers occur twice.

Chalk

because you added 9 to 36 and got 37

gifts total per day:
1
3
6
10
15
21
28
36
45
55
66
78
----
364

/me walks away

seamus

seansouth wrote:

Did you really feel the need to post what you posted?

I am asking a legitimate question, and showing why I asked it.

Wow. Touchy aren't we? You didn't provide any evidence as to *why* you asked it

Because the same sum is done twice, the same numbers occur twice.

Still don't understand.

denachoman

Where did you do Maths, Seansouth?

You made a couple of mistakes in the second part where you came up with 321.

On day 9 he received 45 gifts, not 37.
So total = 120 + 45 = 165

Day 10:
total = 165 + 55 = 220

Day 11:
total = 220 + 66 = 286

Day 12:
total = 286 + 78 = 364

Which is the same as the toal in the 1st part.


Slow day here too.......

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seamus wrote:

You didn't provide any evidence as to *why* you asked it

I asked it because I was wondering where I was going wrong.

seamus wrote:

Still don't understand.

Well have a look at the first six days, they have the same totals as the last six, in descending order. So adding the first six, then multiplying by 2 would be like adding the first six, then adding the last six, then adding the results together.

seamus

seansouth wrote:

I asked it because I was wondering where I was going wrong.

Well have a look at the first six days, they have the same totals as the last six, in descending order. So adding the first six, then multiplying by 2 would be like adding the first six, then adding the last six, then adding the results together.

Heh, I wasn't looking at the numbers

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denachoman wrote:

Where did you do Maths, Seansouth?

denachoman wrote:

You made a couple of mistakes in the second part where you came up with 321.

On day 9 he received 45 gifts, not 37.
So total = 120 + 45 = 165

Day 10:
total = 165 + 55 = 220

Day 11:
total = 220 + 66 = 286

Day 12:
total = 286 + 78 = 364

Which is the same as the toal in the 1st part.

Thank you very much.

ixoy

But can all of this be expressed as a mathematical function? Is there some sort of Geometric/Inductive series in there that can fit on one line? Algorirthimically it'd be easy to program recursively but there's got to be a way to express it elegantly in a sum - can anyone see it?

Guess what: slow day here too!

Flukey

Where the hell is he going to put it all is the real question? It could cause all sorts of other problems too. Remember Frank Kelly's Christmas Countdown?

Chalk

for x = 1 to 12 do
total := total+x+1

Lump

Ask Ecksor, he's the maths god.... there's a rather large section of leaving cert maths that does all this, ****ed if I remember. Probability was one half.... what you're talking about is the other half or that kind of stuff AFAIK.


John

Fudger

seansouth wrote:

Did you really feel the need to post what you posted?

Why yes..... yes i did............

Carbo

For x = 1 to 12,

Total = the sum of x multiplied by 13-x

Maths is great.

cajun_tiger

1+2+3+4+5+6+7+8+9+10+11+12=78

wasn't the song what he got each day and then listed off what he had as a corus??

ixoy

The answer can be found here.

n=6
2.Σn.(13-n)
n=1

The reasoning is in the link above....

However, that works on the symmetrical properties of there being 12 days of Christmas - as SeanSouth did. If you want to find out the number of presents accumulated on any day of Christmas - including a hypothetical 13th or 201st day, then you can apply this formula:

( N + 2)
( 3 ) .. where n=the day of Christmas.

Apparently this means that, if every day were Christmas, you'd accumulate 8,171,255 gifts...

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seansouth wrote:

Now assuming on each day, the singer receives what he sings on each day, how many gifts will he have ended up with by the twelfth day?

I know what you are saying Cajun, but that would be no fun!

pickarooney

Does a partridge in a pear tree not count as two gifts?

Spunog UIE

seansouth wrote:

Now assuming on each day, the singer receives what he sings on each day, how many gifts will he have ended up with by the twelfth day

haha, ye...but he doesn't. Christmas does strange things to some people, shouldn't you be getting your turkey?

cajun_tiger

On the first day of Christmas,
my true love sent to me
A partridge in a pear tree. =2

On the second day of Christmas,
my true love sent to me
Two turtle doves,
And a partridge in a pear tree.=4

On the third day of Christmas,
my true love sent to me
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =7

On the fourth day of Christmas,
my true love sent to me
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =11

On the fifth day of Christmas,
my true love sent to me
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =16

On the sixth day of Christmas,
my true love sent to me
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =22

On the seventh day of Christmas,
my true love sent to me
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =29

On the eighth day of Christmas,
my true love sent to me
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =37

On the ninth day of Christmas,
my true love sent to me
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =46

On the tenth day of Christmas,
my true love sent to me
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =56

On the eleventh day of Christmas,
my true love sent to me
Eleven pipers piping,
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree. =67

On the twelfth day of Christmas,
my true love sent to me
Twelve drummers drumming,
Eleven pipers piping,
Ten lords a-leaping,
Nine ladies dancing,
Eight maids a-milking,
Seven swans a-swimming,
Six geese a-laying,
Five golden rings,
Four calling birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree!79

79+67+56+46+37+29+22+16+11+7+4+2=376

Chalk

hahah your nuts

did you type that out yourself?

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pickarooney wrote:

Does a partridge in a pear tree not count as two gifts?

That's a whole nother can of worms!

Agent Smith

this is WAY over my head, but i second the call for ecksor, the maths god

ixoy

agent smith wrote:

this is WAY over my head, but i second the call for ecksor, the maths god

But there's no need - I posted a link to the answer Using two formulas! It's done and dusted....

cajun_tiger

no i didn't type it out but yes i am nuts