Several children were playing in the ugly tree when suddenly they all fell.
Roger hit branches A, B, and C in that order on the way down.
Sue hit branches D, E, and F in that order on the way down.
Gillian hit branches G, A, and C in that order on the way down.
Marcellus hit branches B, D, and H in that order on the way down.
Juan-Phillipe hit branches I, C, and E in that order on the way down.
Mikey hit every branch A through I on the way down. Given only this information, in
how many different orders could he have hit these 9 branches on the way down?

$\displaystyle gabicdefh$
$\displaystyle gaibcdefh$
$\displaystyle giabcdefh$
$\displaystyle igabcdefh$

Thanks. So those are the only four orders?

Unless others find more!

Thanks. Is there a reason that you put all the gs first? I mean why could it not just be abcdefgh? Once again thanks a lot

G>A>C

This got me curious. Is there a truly mathematical way of developing an answer? Just a curiosity. I was wondering if somehow you could list the branches in order, and resolve an answer without manually counting all of the possibilities.

Yes there is a way to develop the answer mathematically. Word the question like this.

Mikey has 9 cards in front of him, in how many different ways can he pick up the 9 cards?

Well....

1,2,3,4,5,6,7,8,9
1,2,3,4,5,6,7,9,8
1,2,3,4,5,6,8,9,7
ect. You should have been taught about factorials. The factorial of a number is calculated as.

$\displaystyle 9! = 1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9$

You'll most certainly need a calculator because factorials grow at an insane rate for each digit you add. Go ahead and type that into your calculator.

P.S The branch example is a terribly worded question because one can assume you can't hit branch I before hitting branch A. So if one falls one can only hit the branches in letter order progressing alphabetically.

Originally Posted by MaxJasper
$\displaystyle gabicdefh$
$\displaystyle gaibcdefh$
$\displaystyle giabcdefh$
$\displaystyle igabcdefh$
It seems to me there are some missing possibilities.

I G A B D H C E F

for example?

10. ## Reply - part 1

Hello, Makaveli!

Several children were playing in the ugly tree when suddenly they all fell.
Roger hit branches A, B, and C in that order on the way down.
Sue hit branches D, E, and F in that order on the way down.
Gillian hit branches G, A, and C in that order on the way down.
Marcellus hit branches B, D, and H in that order on the way down.
Juan-Phillipe hit branches I, C, and E in that order on the way down.
Mikey hit every branch A through I on the way down.
Given only this information, in how many different orders
could he have hit these 9 branches on the way down?

I have this diagram.
Reading from left to right, we have the branches from the top down.

$\displaystyle \begin{array}{ccccccccccc}&&&& I \\ &&&&& \searrow \\ &&&&&& C \\ &&&&& \nearrow && \searrow \\ G & \to & A & \to & B &&&& E & \to & F \\ &&&&& \searrow && \nearrow \\ &&&&&& D \\ &&&&&&& \searrow \\ &&&&&&&& H \end{array}$

We know that $\displaystyle I$ is somewhere above $\displaystyle C.$
$\displaystyle I$ could be above $\displaystyle G$, between $\displaystyle G$ and $\displaystyle A$, between $\displaystyle A$ and $\displaystyle B$, or between $\displaystyle B$ and $\displaystyle C.$

We know that $\displaystyle D$ is between $\displaystyle B$ and $\displaystyle E.$
$\displaystyle D$ could be between $\displaystyle B$ and $\displaystyle C$ or between $\displaystyle C$ and $\displaystyle E.$
. . [To be continued]

11. ## Re: Reply - part 2

We know that $\displaystyle H$ is below $\displaystyle D.$
$\displaystyle H$ could be between $\displaystyle D$ and $\displaystyle E$, between $\displaystyle E$ and $\displaystyle F$, or below $\displaystyle F.$

There are more than 4 possible orders.

Once again, the program would not let me complete my post.
I clicked on PREVIEW and got a preview of what I had styped.
But my work screen was blank and frozen.
I could not enter anything on it.

Would a simple nCr function work to some extent, to help to figure out the number of combinations maybe ?

Could someone please figure this out and show me how they got the answer please? My test is on Sunday, I have to go into school to take it. Thanks so much.