Christmas Calculus question (riddle?) lol, please help :)

[Calculista222]

I have no clue how to begin this problem, I have gotten no way but I have tried.

Here it goes --- (any help or starter work is greatly appreciated) ---

1.) Recall the traditional Christmas Carol "the twelve days of Christmas"

The total number of gifts is 364 gifts. Suppose the 'true love' wants to reciprocate the sentiment but for the enter *leap year*

Let us label the gifts G[sub:2l545jpu]1[/sub:2l545jpu] , G[sub:2l545jpu]2[/sub:2l545jpu] , G[sub:2l545jpu]3[/sub:2l545jpu] ....G[sub:2l545jpu]366[/sub:2l545jpu]

Where n * G[sub:2l545jpu]n[/sub:2l545jpu] are presented on the n[sup:2l545jpu]th[/sup:2l545jpu] day of the year and every subsequent day.


Which gift(s) did the "true love" get the most of, how many?

Which gift(s) did the true love" get the least of and how many?

[there may be multiple solutions]









Please help, No idea where to start this. :!:

 

[Deleted member 4993]

Re: Christmas Calculus question (riddle?) lol, please help :

I have no clue how to begin this problem, I have gotten no way but I have tried.

Here it goes --- (any help or starter work is greatly appreciated) ---

1.) Recall the traditional Christmas Carol "the twelve days of Christmas"

The total number of gifts is 364 gifts. Suppose the 'true love' wants to reciprocate the sentiment but for the enter *leap year*

Let us label the gifts G[sub:3ck10o28]1[/sub:3ck10o28] , G[sub:3ck10o28]2[/sub:3ck10o28] , G[sub:3ck10o28]3[/sub:3ck10o28] ....G[sub:3ck10o28]366[/sub:3ck10o28]

Where n * G[sub:3ck10o28]n[/sub:3ck10o28] are presented on the n[sup:3ck10o28]th[/sup:3ck10o28] day of the year and every subsequent day.


Which gift(s) did the "true love" get the most of, how many?

Which gift(s) did the true love" get the least of and how many?

[there may be multiple solutions]









Please help, No idea where to start this. :!:

Start with defining variables - naming what you need to find.

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[soroban]

Re: Christmas Calculus question (riddle?) lol, please help :

Hello, Calculista222!

Recall the traditional Christmas Carol "The Twelve Days of Christmas".
The total number of gifts is 364 gifts.

Suppose I want to reciprocate the sentiment, but for the entire leap year.

Let us label the gifts: .\(\displaystyle G_1,\:G_2,\:G_3,\:\hdots\:G_{366}\)

. . where \(\displaystyle n\cdot G_n\) gifts are given on the \(\displaystyle n^{th}\)day of the year and every subsequent day.


(a) Which gift(s) did my true love get the most of, and how many?

(b) Which gift(s) did my true love get the least of, and how many?

Crank out a few terms of the list . . .


\(\displaystyle \text{Day 1:}\quad\;\; 1\!\cdot\!G_1\)

\(\displaystyle \text{Day 2:}\quad\;\;1\!\cdot\!G_1 + 2\!\cdot\!G_2\)

\(\displaystyle \text{Day 3:}\quad\;\; 1\!\cdot\!G_1 + 2\!\cdot\!G_2 + 3\!\cdot\!G_3\)

. . \(\displaystyle \vdots\). . . . . . . . . . . . . \(\displaystyle \vdots\)

\(\displaystyle \text{Day 366: }\;1\!\cdot\!G_1 + 2\!\cdot\!G_2 + 3\!\cdot\!G_3 + . . . + 366\!\cdot\!G_{366}\)


The total is:

. . \(\displaystyle (366\!\cdot\!1)G_1 + (365\!\cdot\!2)G_2) + (364\!\cdot\!3)G_3 + \hdots + (2\!\cdot\!365)G_{365} + (1\!\cdot\1366)G_{366}\)


The coefficients are the product of two numbers whose sum is a constant, 367.
. . The maximum product occurs when the two factors are "most equal".

There are two cases: .\(\displaystyle (184\!\cdot\!183)G_{183}\,\text{ and }\,(183\!\cdot\!184)G_{184}\)

. . (a) My true love got a maximum of 33,672 each of \(\displaystyle G_{183}\) and \(\displaystyle G_{184}.\)


The minimumn product occurs when the two factors are "least equal".

There are two cases: .\(\displaystyle (366\!\cdot\!1)G_1\,\text{ and }\,(1\!\cdot366)G_{366}\)

. . (b) My true love got a minimum of 366 each of \(\displaystyle G_1\) and \(\displaystyle G_{366}.\)

 

[Calculista222]

Re: Christmas Calculus question (riddle?) lol, please help :

Soroban, I can not thank you enough.

You were the most helpful to me while the other jerks either did not reply or gave bullcrappy answers.


<3 thank yew