# Thread: Urgent algebra homework! Xmas stuff... :D

1. ## Urgent algebra homework! Xmas stuff... :D

Despite the season being over I am still left puzzled over this problem.

The following questions are related to the popular Christmas song "The Twelve Days of Christmas".

We all know it's fairly simple to figure out the amount of presents found over the twelve days of Christmas. It is 364 presents.

How many ways did you find to solve for 364 presents?

Tough what about Twelve Days of Christmas? How many presents would we receive then?
And the toughest of them all THE nth day of Christmas? How on Earth are we supposed to explain and work out the nth day of Christmas?

Help needed.
Thanks!

2. Originally Posted by chocole
Despite the season being over I am still left puzzled over this problem.

The following questions are related to the popular Christmas song "The Twelve Days of Christmas".

We all know it's fairly simple to figure out the amount of presents found over the twelve days of Christmas. It is 364 presents.

How many ways did you find to solve for 364 presents?

Tough what about Twelve Days of Christmas? How many presents would we receive then?
And the toughest of them all THE nth day of Christmas? How on Earth are we supposed to explain and work out the nth day of Christmas?

Help needed.
Thanks!

Tiina
Maybe I am not familiar with the version you know. If you get 1 present on the first day, 2 presents on the 2nd day, and n presents on the nth day, then your total is:

$\sum_{i=0}^n i = \frac{n(n+1)}{2}$

3. Originally Posted by colby2152
Maybe I am not familiar with the version you know. If you get 1 present on the first day, 2 presents on the 2nd day, and n presents on the nth day, then your total is:

$\sum_0^n i = \frac{n(n+1)}{2}$
The problem states how many presents would be received over any other number (n) of days.

I am brain dead. I've never been this stuck... on this kind of problem. XD

4. Originally Posted by chocole
The problem states how many presents would be received over any other number (n) of days.

I am brain dead. I've never been this stuck... on this kind of problem. XD
The formula for the sum of an arithmetic series is:

$S_{n} = \frac{n}{2} \left( 2a + (n - 1)d \right)$

a = 1 and d = 1

So:

$S_{n} = \frac{n}{2} \left( 2 + (n - 1) \right)$

$S_{n} = \frac{n}{2} \left( n + 1 \right)$

$S_{n} = \frac{n^2 + n}{2}$

Where n = the number of days.

So on the 1st day you would have 1 present, on the 2nd day, you would receive 3 presents, etc...

5. Hello, chocole!

The following questions are related to the Christmas song "The Twelve Days of Christmas".

We all know how to figure out the number of presents given over the 12 days.
It is 364 presents.

How many ways did you find to solve for 364 presents?

$\begin{array}{cccc}\text{Day} & & \text{Presents} \\
1 &1 & 1 \\
2 & 1+2 & 3 \\
3 & 1+2+3 & 6 \\
4 & 1+2+3+4 & 10 \\
\vdots & \vdots & \vdots
\end{array}$
. These are "triangular numbers."

On the $n^{th}$ day, my true love gave to me: . $\frac{n(n+1)}{2}$ gifts.

By the $n^{th}$ day, my true love gave to me a total of:

. . $\sum^n_{k=1}\frac{k(k+1)}{2} \;=\;\frac{n(n+1)(n+2)}{6}$ gifts.