1. Subscribervenda
    Dave
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    26 Dec '21 10:10
    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
  2. Standard memberBigDogg
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    26 Dec '21 10:57
    @venda said
    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
    Wouldn't that be a sum?

    As in 1+2+...+11+12 = 78
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    26 Dec '21 16:03
    @bigdogg said
    Wouldn't that be a sum?

    As in 1+2+...+11+12 = 78
    I think you and I talked about this before. To add 1-100 you can
    101x50
    So
    13x6=78
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    26 Dec '21 21:201 edit
    With a series this short does it really matter?
  5. Subscribervenda
    Dave
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    26 Dec '21 23:31
    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
  6. Joined
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    27 Dec '21 01:491 edit
    @venda said
    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
    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.
  7. Standard memberBigDogg
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    27 Dec '21 03:04
    @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
  8. Standard memberBigDogg
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    27 Dec '21 03:19
    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.

    Reveal Hidden Content
    Formula: (n/6)(n+1)(n+2) = number of gifts


    But does it really work?
    Reveal Hidden Content
    (12/6)*13*14 = 364 -- yup
  9. Subscribervenda
    Dave
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    27 Dec '21 11:481 edit
    @bigdogg said
    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]
    Excellent Mr Dogg
    That is what I was after
    But how is the 6 derived?
  10. Standard memberBigDogg
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    27 Dec '21 13:43
    @venda said
    Excellent Mr Dogg
    That is what I was after
    But how is the 6 derived?
    The article explains that in the "General Formula" section.
  11. SubscriberSuzianne
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    29 Dec '21 08:39
    @eladar said
    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.
    Maybe you should give the song another listen.

    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 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.
  12. Subscribervenda
    Dave
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    29 Dec '21 14:14
    @suzianne said
    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.
    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 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
  13. Subscribersonhouse
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    01 Jan '22 19:28
    @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🙂
  14. Joined
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    01 Jan '22 20:091 edit
    @venda said
    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
    https://www.clickondetroit.com/news/2021/12/10/how-much-do-the-12-days-of-christmas-actually-cost/


    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.
  15. Subscribersonhouse
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    01 Jan '22 20:36
    @Eladar
    Yep, you should know ALL about pushing fake BS.
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