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#176 2011-01-18 17:17:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Hi gAr;

That is right. Very good. I do not have a nice clean formula either.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#177 2011-01-18 18:11:02

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi bobbym,

At first I thought I could rearrange the longer paths to make the computation easy, but was disappointed to find out they give different answers...


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#178 2011-01-18 20:22:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

I have a method that works for one open street. I cannot as of yet generalize to more. The literature is also sketchy.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#179 2011-01-18 21:55:44

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Yes, I too could not find much information regarding this.
In fact I too did not think of this when I came across the square grids' problem!
But, since the no. of paths are less than the available paths in square grids', I guess we should subtract some value.
Maybe we will get more insight when we plot the total paths vs no. of open paths, the effect of rearranging open paths etc.
I'll leave it for now!

Last edited by gAr (2011-01-18 21:57:33)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#180 2011-01-26 18:22:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

New problem:

A guy has a scale with two pans. On the left pan he has a block weighing 196 gms. He has bolts that weigh 67 gms, nuts that weight 41 gms and washers that weigh 30 gms. He would like to level the two pans, that is have equal weights in both.

A) If he has 10 of each type what is the smallest weight he can have on a pan?

B) If he has an unlimited amount of each what is the smallest then?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#181 2011-01-26 19:55:10

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi bobbym,

Last edited by gAr (2011-01-26 19:55:35)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#182 2011-01-26 20:42:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Hi gAr;

First let me say how sorry I am that everyone had to be part of that ugly affair today. I hope it is finally over.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#183 2011-01-26 20:54:34

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi bobbym,

I was getting a feeling whether it was a bot for flaming!
http://en.wikipedia.org/wiki/Chatterbot

And for that weights' problem, is there a way other than brute force?

Last edited by gAr (2011-01-26 20:57:34)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#184 2011-01-26 21:04:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Hi;

I am pretty sure he is real but then who knows.


For a good solution? Not yet!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#185 2011-01-26 21:35:19

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi,

It is a Partition problem, isn't it?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#186 2011-01-26 21:46:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Yes, for every possible weight that can be on the left pan. That complicates it. If it were just a constant weight on the left pan then it would be an ordinary generating function.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#187 2011-01-26 21:56:43

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Oh, can generating function be used for constant weight on one pan? Please tell me about it...


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#188 2011-01-26 22:11:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Enter into Sage:

And expand the answer. What you will get is the number of solutions of:

30 a + 41 b + 67 c = r with 0 ≤ a,b,c ≤ 10.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#189 2011-01-26 22:21:03

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Thanks!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#190 2011-01-26 22:24:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

What it tells you for instance is that there is only 1 way using the 10 of each type to make a 340 gm weight. Because the coefficient in front of x ^ 340 is 1. You can also say that the number of partitions of 340 from the set of 10 30's and 10 41's and 10 67's equals 1.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#191 2011-01-26 22:34:27

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Nice smile


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#192 2011-01-29 16:28:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

A teacher gives a test. No partial credit is given. There are 9 5 point questions, 7 4 point questions and  3 9 point questions. A student who has a 57% chance of passing, a 21% chance of getting between 80 - 90 and 2% chance of getting better than 90 claims he got a 93. What are the odds of that happening?

A says) 12% chance he is telling the truth.
B says) 13% chance he is lying.
C says) No way baby!
D says) He looks honest so he must be truthful.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#193 2011-01-29 20:42:04

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi bobbym,

Can we do it without knowing the credit points for passing?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#194 2011-01-29 20:57:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Hi gAr;

Yes but if it will help the chance of him receiving a passing grade is over 90%. Try to think out of the box on this one because it is devilishly sadistic but it does have an answer.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#195 2011-01-29 21:05:45

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi,

Hmm, I was looking at the frequency plot of possible credits. Reading your reply, I think it must be simpler than that!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#196 2011-02-02 06:18:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Hi gAr


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#197 2011-02-02 06:30:13

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi bobbym,

Last edited by gAr (2011-02-02 14:33:30)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#198 2011-02-02 06:44:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

Hi gAr;

I do not know how that got in there. I checked my notes and it is correctly stated there.

I consider that you solved it! For understanding that shows you solved it! Very good. Excellent work. You can erase your answers and hide the correct one in the previous post. I am sorry, it can only be a typo. I have amended the problem. Again, very good solution!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#199 2011-02-02 06:56:31

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Is this cool with you?

Hi bobbym,

No problem, accidents happen.
I have just hidden the original answer, I hope you won't mind.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#200 2011-02-02 07:02:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,177

Re: Is this cool with you?

That is okay with me but I changed the original problem so anyone else will not hangup. So you can put the answer to the correct one or that instead, whatever you like. You have a free pass to do whatever you want.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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