Thread: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

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?

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.



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

It seems to me there are some missing possibilities.

How about

I G A B D H C E F

for example?

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.




We know that is somewhere above
could be above , between and , between and , or between and

We know that is between and
could be between and or between and
. . [To be continued]

We know that is below
could be between and , between and , or below

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.