Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Oh, that explanation works fine because it is true. You see the problem for n x n rather than n x m is much better solved and documented. No one wants to work on the the n x m. Anyway, I thought since I could easily calculate ( 20 , 20 ) all I had to do was store that number, then  ( 20 , 20 ) becomes ( 0 , 0 ) and now what is left? The problem is ( 0 , 0 ) to ( 0, 10 ) which is 2^9 ways. So multiply the two numbers and you have the answer to ( 0 , 0 ) to ( 20 , 30 ). Right? Nope, that did not work!

And just now, I see the big hole in that analysis, why it did not work.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Hi bobbym,

I think doing like that misses many paths!
E.g., you're not considering moving to (0,30) ?

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

That is right! When we do that in an ordinary lattice problem such as ( 0,0 ) to ( 3,3) to ( 10,10 ) it is okay to compute the paths from
( 0,0 ) to ( 3,3) and then multiply by the paths from ( 0,0 ) to ( 7,7). There we only make one unit moves at a time.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

For 2x1 grid, I'm able to find only 3 ways instead of 5, with that condition of moving only up or right.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi gAr;

u, u, r
u, r, u
r, u, u
2u, r
r, 2u

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Oh, okay.
I missed the condition "can move any number of vertices".

Though I did not think of a rook walk, I did use grids.
I wrote the numbers which I calculated along the vertices, and conjectured the formula to be of the form:

f(m,n) = a*f(m-1,n)+b*f(m,n-1)+c*f(m-1,n-1)+d

Then chose different values which I calculated and solved the simultaneous equations.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Hi;

That is the right way to use experimental math.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

That's a great way, I think!

Knuth has said it somewhere, concrete mathematics I guess, to conjecture a formula prove it by induction is a way to do.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Yep! Guess at a form and prove it later. Or use a computer to get the answer and then work backwards.

Remember what he said about "low hanging fruit?"

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Right!

If Euler had today's computer, Opera omnia would have passed 760 volumes instead of 76  !

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

That dude continued to write and do math after he went blind! There is not a piece of math that does not have Euler's name somewhere in it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Yes, really awe-inspiring!

That lion left his claw marks everywhere!!

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

So, you know that quote?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Yes, I have read Newton's biography.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

You know, when I mentioned that quote to a MIT graduate student in mathematics he did not know it. Had never heard of it!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Maybe he's going to become a manager!

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

A manager of what?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

I don't know.
I meant he's not focused on science and technology, and may go for an MBA.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Actually he is a full fledged mathematician. They just do not study the history of anything anymore.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

Oh, I didn't know he's a mathematician.
Even I'm not interested in history, but if it's related to science and math I like 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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

When you read math books lots of them have the history of the famous mathematicians.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

I remember I read a graffiti in "concreate mathematics", something like this-

"A few days ago I was reading what Gauss had done during his kindergarten, now I'm reading what is beyond his PhD. Is this intimidating or what?"

Very funny!

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

Does he think he is passed Gauss?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Is this cool with you?

I don't know.

That's all what was written in the margin.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is this cool with you?

What do you think he was trying to say?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.