Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Number of combinations

Me too. I am hoping I never see another problem like this again.

I am going to take a little break to eat, see you later.

---

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: Number of combinations

Ok, see you later.

---

"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: Number of combinations

Hi gAr;

I solved the problem! There are really only 2 types of pairs. The ZT type which we know have 72 ways and the AB, CD, EF, GH, type which are the same.

There are 40 ways to arrange {1,2,3,4},{0,1,2,3,4,5,6,7,8,9}, so we enumerate them.

We count up the number of evens in each pair and put it on top of the pair.

This is the number of evens in each pair.

There are 10 zeros, 20 ones and 10 twos.

From this list we make up the partitions of 5,4,3 evens in the 4 pairs.

5 evens in ( AB, CD, EF, GH)

Calculating them one row at a time.

216000+273600 =489600 ways to have 5 evens in the 4 pairs.

4 evens in ( AB, CD, EF, GH)

Calculating them one row at a time.

48600 + 456000 + 116280 = 620880 ways to have 4 evens in the 4 pairs.

3 evens in ( AB, CD, EF, GH )

Calculating them one row at a time.

216000+273600 =489600 ways to have 3 evens in the 4 pairs.

Now taking into account ZT.

---

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: Number of combinations

Hi bobbym,

Nice one!
I'm glad that you solved 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: Number of combinations

Hi gAr;

Thanks! How are you today?

---

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: Number of combinations

Hi,

I'm fine.
How are you?

---

"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: Number of combinations

Everything appears okay. Good to be doing some math again.

---

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: Number of combinations

Yes, doing math is always good!

---

"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: Number of combinations

I am looking at some videos on sequences and convergence. Pretty basic stuff but
better than tv.

---

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: Number of combinations

On youtube?

---

"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: Number of combinations

Yes,

http://www.youtube.com/watch?v=_NmSEEht … ure=relmfu

Pretty basic but I still learned some things about Fibonacci.

---

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: Number of combinations

Okay, I see..

---

"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: Number of combinations

I read he was only able to borrow a math book for 1 week. That was his entire math education!
And still he is a genius.

---

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: Number of combinations

Is it? Cool!
I haven't seen the video yet.

Now he can read anything online!

---

"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: Number of combinations

Yes! We are lucky! People today are lucky and they do not even know it.

In his book in 1225 he first mentions the relationship between the odd numbers
and the squares. But he had no notation to write it in. Even the = sign was not yet
invented!

---

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: Number of combinations

Yes, but not all people are interested in knowledge!

I was checking this: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormulae.html

Contains many identities which I didn't know.
E.g.:

!!!

---

"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: Number of combinations

Hi gAr;

There is a magazine called the Fibonacci quarterly. There are many formulas involving
the fibonacci numbers and new ones are found each day.

Thanks for providing that link.

---

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: Number of combinations

Hi bobbym,

I think I have heard about that before.
Do you subscribe 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: Number of combinations

No, but I used to go down to the university and look at it. Now I am further away and do not get to see 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: Number of combinations

Okay, it's good to live nearby a university/library.

---

"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: Number of combinations

I used to go down there and study a lot. Then the internet began to be
a better place. So I did not use it as much.

I am going to take a break, see you later.

---

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: Number of combinations

Ok, see you later.

---

"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."