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#1 2013-09-29 04:42:06

jacks
Member
Registered: 2012-11-21
Posts: 77

no. of path in Grid

In a Diagram shown in figure, Not that the Grid path from F to G is missing.

So path from A to B can not pass from F and G.

How many path are there from A to B 

assume all path only have steps going up or to the right.

View Image: Grid3.jpg

Last edited by jacks (2013-09-29 05:30:44)

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#2 2013-09-29 04:51:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

Where is D and E?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-09-29 05:31:38

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

Sorry Bobbym , actually it is A and B

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#4 2013-09-29 05:36:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

Hi;

I am getting 38 ways.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#5 2013-09-29 05:37:28

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

Would you like to explain it to me, Thanks

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#6 2013-09-29 06:03:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

For ones that have missing intersections and are small the vertex counting method will work fine.

The drawing shows the number of paths to each node.

Each node is the sum of the two nodes underneath and to left of it.

View Image: 2013-09-29_110006.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#7 2013-09-29 06:37:43

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

Thanks Bobbym Got it.

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#8 2013-09-29 06:54:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

There is an analytical answer for these type but the counting method is easier to understand.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#9 2013-09-29 07:02:25

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

Would you like to explain me analytical answer.

I also tried for that method but could not get it.

(But I like yours Counting method.)

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#10 2013-09-29 09:45:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

Hi;

By combinatorics:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#11 2013-09-30 06:36:07

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

Thanks Bobbym would you like to explain me to it.

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#12 2013-09-30 06:38:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

It is just adding up all the paths in the lattice around the missing intersection.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#13 2013-09-30 06:47:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: no. of path in Grid

Hi

is also a way.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#14 2013-09-30 07:16:01

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

To anonimnystefy I have understand 

(Which is Total no. of path from A to B, If There is a connectivity between F to G)

but Did not understand

Would you explain it to me.

Thanks

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#15 2013-09-30 07:17:51

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: no. of path in Grid

It's the number of paths from A to F times the number of paths from G to B.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#16 2013-09-30 07:24:50

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

To Admin (Bobbym) i did not understand it

It is just adding up all the paths in the lattice around the missing intersection.

Thanks

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#17 2013-09-30 07:28:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: no. of path in Grid

I think I know which points he took, but I cannot be sure.

I think he used (2,3), (3,0) and (3,1), A being (0,0) and B being (5,4).


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#18 2013-09-30 07:32:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

Hi;

Look at my drawing in post #6.

I picked (2,3), (3,1) and (4,0) and calculated the paths from there.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#19 2013-09-30 07:33:05

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

It's the number of paths from A to F times the number of paths from G to B.

To anonimnystefy I did not understand it

why we minus it.

please explain it to me

Thanks

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#20 2013-09-30 07:46:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: no. of path in Grid

anonimnystefy wrote:

It's the number of paths from A to F times the number of paths from G to B.

This is the reason. These are all the paths that become unavailable when we remove the line.

Hi bobbym

Yes, I meant (4,0).

Last edited by anonimnystefy (2013-09-30 07:59:54)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#21 2013-09-30 07:57:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

Hi;

I did not see your post 17, I was answering his question.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#22 2013-09-30 08:03:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,859

Re: no. of path in Grid

Even better then.

I guess the question is fully answered now. Three ways is enough.

I just want to try to do one more thing.

Last edited by anonimnystefy (2013-09-30 08:04:30)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#23 2013-09-30 09:54:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

There is another more general way. That maybe can answer for many missing intersections.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#24 2013-10-13 16:55:01

jacks
Member
Registered: 2012-11-21
Posts: 77

Re: no. of path in Grid

Thanks Admin and anonimnystefy got it

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#25 2013-10-13 17:15:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,564

Re: no. of path in Grid

Hi;

You are wlecome.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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