Can someone explain the 12 Days of Christmas puzzle to me please?

Question

I saw a quiz where you had to derive the total number of gifts received when the "12 Days of Christmas" is sung in it's entirety. I read an explanation but don't understand it!
The correct answer is 364 and on the 12th day a total of 78 items are received. Can someone please explain this in the simplest possible terms please? Remember we are counting items and not gifts therefore 5 gold rings is 5 items. Please don't post the Wikipedia thing....I don't understand that either!

Answer 1

The explanation of coming up with 364 has already been given.

If you take a close look, you will find it to be a trick question!

If you omit duplicate gifts, the actual answer is 86 items not 78!

5 golden rings
23 birds
50 people and
8 cows.

Don't forget that those "8 maids a milking" were milking SOMETHING!

You might also want to count the drums, drumsticks and bagpipes separately from the people playing them.

That would bring the answer up to:
86 + 11 + 12*3 =
97 + 36 =
133

EDIT:
I stand corrected!
I forgot about the pear tree.
Add 1 to my values.
.

Answer 2

When you add up the sum of N numbers, the answers comes
out to (N+1)*N/2

So for twelve, you get 13*12/2 = 13*6 = 78.

As for why this is so, think of pairing the first and last numbers:

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

You stop at this point because you have accounted for all
the numbers. Note that each sum adds up to 13, which is
where the N+1 in the formula comes from. As you work
you way up the list, you are done when you have accounted
for all the numbers, which happens after you have gone
halfway up the list. This is where the N/2 part of the
formula comes from. It works just as well when N is odd
as it does when N is even.

Answer 3

The "correct" answer is 376, not 364. Most people forget that on the first day of Christmas, the unlucky recipient of these gifts actually gets two items- a partridge AND a pear tree.
You need to get a sheet of A4 paper and a pencil, and once you have written down what is happening on each successive day, you'll soon understand the answer!
Day one- a partridge and a pear tree arrives. Total gifts = 2
Day two, a partridge, pear tree and two turtle doves arrive. The total number of gifts on day two is 4 (partridge+pear tree +2 doves). BUT there are already 2 gifts from day one in the house, so there are now 4 + 2 items there (specifically two partridges, two pear trees and two turtle doves. There are 6 gifts in the house.
On day three, add three new gifts, along with a new set of two turtle doves and a partridge and a pear tree.
This will make 3+2+1+1 gifts arriving on day 3 (that's 7)
To this number now has to be added the number already in the house, 6. So now there are 6+7 gifts in the house. (that is 13).
OK? So get cracking on the remainder of the days.
As a check, you should find that day 4 will have
4+3+2+1+1+(all those gifts accumulated since the first day)
That is 4+3+2+1+1+13 (=24)
Day 5 will have 5+4+3+2+1+1+24 = 40
Day 6 will have 6+5+4+3+2+1+1+40
and so on!!

Answer 4

Throughout the song, you get 1 + (1+2) + (1+2+3) + (1+2+3+4).....(1+2+3+4+5+6+7+8+9+10+11+12).

I'm sure there's a wonderful equation that would let you do this easily, but I'm not enough of a math person to figure that one out.

On the last day, you have 12+11+10+9+8+7+6+5+4+3+2+1 = 78.

Answer 5

12 Days Of Christmas Puzzle

Answer 6

On the nth day of Christmas (n=1, 2, ... 12), the number of items received is n(n+1)/2. (Gauss came up with that formula when he was a kid, there's an interesting story behind it.)

We're on the right track, because on the 12th day the number of items received would be 12*(12+1)/2 = 78.

Now we need to calculate the sum of n(n+1)/2 from n=1 to 12.

sum{n(n+1)/2} = sum{(n*n+n)/2} = (sum(n*n)+sum(n))/2

Now sum(n) from 1 to k = k(k+1)/2 using the same formula as above, and sum(n*n) from 1 to k = k(k+1)(2k+1)/6. So the total number of gifts up to day k is

{k(k+1)/2 + k(k+1)(2k+1)/6}/2

Substitute k=12 and you get your answer, 364.

Answer 7

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RE:
Can someone explain the 12 Days of Christmas puzzle to me please?
I saw a quiz where you had to derive the total number of gifts received when the "12 Days of Christmas" is sung in it's entirety. I read an explanation but don't understand it!
The correct answer is 364 and on the 12th day a total of 78 items are received. Can someone please...

Answer 8

day 1, 1 gift
day 2, 3 gifts ( 1 + 2),
day 3, 1+2+3 or 6 gifts
keep up in this pattern, then add all the final gifts.

it works.