@venda saidWouldn't that be a sum?
We had a question in an xmas quiz which is really easy to work out "longhand" but maybe there's a quick way of doing it with a formula:-
In the 12 days of xmas, how many gifts were given in total?
(1*12, 2*11 3*10 etc.)
No Saturday paper this week by the way
As in 1+2+...+11+12 = 78
@venda saidIt is just 1+2+3+4+5+6+7+8+9+10+11+12.
That's not the question.It's the accumulative gifts as in the song.
I.e on the 1st day a partridge = 1
2nd day 2 turtle doves and a partridge = 3 gifts
3rd day 3 french hens 2 turtle doves and a partridge = 6 gifts and so on
One day 2, 3 gifts were not given. On day 2 only 2 gifts were given.
She did not get 12 partridges and 12 pear trees.
Of course day 1 may actually count as 2 gifts.
27 Dec 21
@venda
In that case, here's the best I can do.
[1*12 + 2*11 + 3*10 + 4*9 + 5*8 + 6*7] * 2
(sequence obviously repeats)
[1*6 + 1*11 + 3*5 + 2*9 + 5*4 + 3*7] * 4
(divide every term inside braces by 2; change outer term to 4)
[6 + 11 + 18 + 36 + 20] * 4
(multiply out small terms)
91 * 4 = 364
27 Dec 21
Found a very nice solution here:
https://www.intmath.com/blog/mathematics/the-twelve-days-of-christmas-how-many-presents-1686
The page derives a formula that works for any number of days. In this case, n=12.
Formula: (n/6)(n+1)(n+2) = number of gifts
But does it really work?
(12/6)*13*14 = 364 -- yup
27 Dec 21
1 edit
@bigdogg saidExcellent Mr Dogg
Found a very nice solution here:
https://www.intmath.com/blog/mathematics/the-twelve-days-of-christmas-how-many-presents-1686
The page derives a formula that works for any number of days. In this case, n=12.
[hidden]Formula: (n/6)(n+1)(n+2) = number of gifts[/hidden]
But does it really work?
[hidden](12/6)*13*14 = 364 -- yup[/hidden]
That is what I was after
But how is the 6 derived?
29 Dec 21
@eladar saidMaybe you should give the song another listen.
It is just 1+2+3+4+5+6+7+8+9+10+11+12.
One day 2, 3 gifts were not given. On day 2 only 2 gifts were given.
She did not get 12 partridges and 12 pear trees.
Of course day 1 may actually count as 2 gifts.
[Verse 1]
On the first day of Christmas, my true love sent to me
A partridge in a pear tree
[Verse 2]
On the second day of Christmas, my true love sent to me
Two turtle doves, and
A partridge in a pear tree
[Verse 3]
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
[Verse 4]
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
[Verse 5]
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
[Verse 6]
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
[Verse 7]
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
[Verse 8]
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
[Verse 9]
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
[Verse 10]
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
[Verse 11]
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
[Verse 12]
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
Big Dogg's equation is exactly correct.
29 Dec 21
@suzianne saidIt wasn't necessary to paste the song.It depends how you interpret the grammar.
Maybe you should give the song another listen.
[youtube]9ZL1u-0Tycc[/youtube]
[Verse 1]
On the first day of Christmas, my true love sent to me
A partridge in a pear tree
[Verse 2]
On the second day of Christmas, my true love sent to me
Two turtle doves, and
A partridge in a pear tree
[Verse 3]
On the third day of Christmas, my true love sent to me
Three fr ...[text shortened]... h hens
Two turtle doves, and
A partridge in a pear tree
Big Dogg's equation is exactly correct.
The gift sequence is repeated every day for the sake of the (may I say very monotonous)song and suggests the gifts were repeated
If not,why doesn't the song simply state the days gift instead of repeating:-
On the second day my true love gave to me 2 Doves
On the 3rd day my true love gave to me 3 hens and so on.
The point of my post was to find a formula for ANY total in an accumulative sequence which is what big dogg did.
If you substitute any number into the equation for the 12 the formula works negating the necessity to multiply 1*12,2*11 etc and adding them up, and so can be used for other purposes in Mathematics other than a pointless song.
Elegant
01 Jan 22
@venda
Well for us folkies, the song is there as a test of memory, all that stuff in the right order and such.
I don't sing much myself, wife does that, I just do instrumentals, guitar, mandolin and the like.
I guess it would be REALLY boring if it was just an instrumental🙂
@venda saidhttps://www.clickondetroit.com/news/2021/12/10/how-much-do-the-12-days-of-christmas-actually-cost/
It wasn't necessary to paste the song.It depends how you interpret the grammar.
The gift sequence is repeated every day for the sake of the (may I say very monotonous)song and suggests the gifts were repeated
If not,why doesn't the song simply state the days gift instead of repeating:-
On the second day my true love gave to me 2 Doves
On the 3rd day my true love gave to me ...[text shortened]... them up, and so can be used for other purposes in Mathematics other than a pointless song.
Elegant
This is the only place I have ever seen anyone suggest there were actually 12 pear trees given.
But hey, any level of idiocy is accepted as truth around here.