Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.**

**Online**

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

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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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**

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

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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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**

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

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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

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)*

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

Hi;

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

For a good solution? Not yet!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi,

It is a Partition problem, isn't it?

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Thanks!

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Nice

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi bobbym,

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi,

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

Hi gAr

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi bobbym,

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

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

Hi bobbym,

No problem, accidents happen.

I have just hidden the original answer, I hope you won't mind.

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**