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#601 2011-02-23 23:04:35

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Nice one !
Can we reduce it to 5x5?
Instead of going from start to O, can it remain in the start state itself? I feel like 5x5 would be a minimized one.


"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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#602 2011-02-23 23:21:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

You could maybe do that but then you need a initial state vector to define where you are starting. It cannot remain in the start state. The act of picking a card will be either a new ace or an other O.

When you calculate say P(n = 10) , you need to do M^10 - M^9, that will take care of overcounting.


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.

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#603 2011-02-23 23:28:03

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Yes, I saw that it overcounted. Got your first answer.
Anyway, a very good problem, 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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#604 2011-02-23 23:34:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Yes to get any n you need just compute M^n - M^(n-1).

Thanks for working on the problem. You did a really nice job.


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.

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#605 2011-02-23 23:44:22

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Thank 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."

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#606 2011-02-26 01:00:17

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,

I did like this using a 5x5 matrix:

To find the probability of picking a different ace during the nth draw is the element [1,4] in P^(n-1), multiplied by 1/52.
E.g., for the fifth draw:

Last edited by gAr (2011-02-26 01:13:40)


"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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#607 2011-02-26 01:19:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi gAr;

Yes, that looks like another way and it saves one less multiplication of the matrix by itself.


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.

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#608 2011-02-26 01:35:49

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,

Yes, and that would be the smallest number of states possible.
I read the document ( the link provided earlier ), and realized that.
Because in P^4, element [1,4] represents the probability of going from the start state to (AAA) in 4 steps. 5th step is getting one more A ( which has probability 1/52 ).

I also discovered that I can produce latex output in sage notebook directly, awesome!


"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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#609 2011-02-26 01:40:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi gAr;

I also discovered that I can produce latex output in sage notebook directly, awesome!

Most CAS have that feature. I use it alot or else I use codecogs or just write it out for small ones.


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.

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#610 2011-02-26 01:49:30

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Great! I didn't know that.
I should've known earlier.


"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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#611 2011-02-28 01:19:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

We have the sequence of squares.

{1, 4, 9, 16, 25, ... }. Somewhere in there is 100 consecutive squares that are equal to the next 99 consecutive squares. What is the smallest value of the first 100?

A says) There is no answer.
B says) I checked and bobbym solved this already so I copied his answer.
C says) Well look again B, his answer is wrong.
D says) I have the correct answer!


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.

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#612 2011-02-28 05:36:19

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,

I assume you mean the sum of the consecutive squares.

Last edited by gAr (2011-02-28 05:41:35)


"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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#613 2011-02-28 05:39:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi gAr;


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.

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#614 2011-02-28 05:44:39

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

I was trying for the past 2 hours thinking average of first 100 = average of next 99, now I read the question again!


"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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#615 2011-02-28 05:54:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

I am so sorry about that? I got mixed up and combined two questions together. It was a stupid mistake. As I said elsewhere. Whenever I do something that dumb, I think of this:

Success is the ability to go from one failure to another with no loss of enthusiasm.

If it is true, I am going to be another Isaac Newton. In return I will give you an easy problem:

The sequence {2,4,6,8,10,12,...n} when one member is removed has an average of 28. What is the smallest n? How many n's are there?

A says) There is no n that works.
B says) There are 3 n's.
C says) There are an infinite number of n's.
D says)  B is finally right! But what is the smallest n? I know!


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.

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#616 2011-02-28 22:13:56

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,

It's ok. I wonder how farther those giants could have seen if they had today's CASs!

Last edited by gAr (2011-02-28 22:15:29)


"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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#617 2011-02-28 22:30:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi gAr;


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.

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#618 2011-02-28 22:40:25

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Oh, 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."

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#619 2011-03-01 01:59:38

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,887

Re: What do you think?

Hi Bobby,

Last edited by phrontister (2011-03-01 15:50:19)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#620 2011-03-01 05:48:08

Howardroark
Member
Registered: 2010-10-10
Posts: 382

Re: What do you think?

Hi bobbym,

bobbym wrote:

The sequence {2,4,6,8,10,12,...n} when one member is removed has an average of 28. What is the smallest n? How many n's are there?

A says) There is no n that works.
B says) There are 3 n's.
C says) There are an infinite number of n's.
D says)  B is finally right! But what is the smallest n? I know!


I come from a civilization which has given the world the number 0..

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#621 2011-03-01 13:37:29

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi Howardroark;

Hi phrontister;

I did not see your answer up there. Very good!


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.

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#622 2011-03-06 06:29:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

New problem:

D wants to use his computer to flip a coin. So he puts a coin on top of the keyboard and goes to bed. The computer has trouble picking up the coin so D decides to build robotic arms for it. Someone tells D about programming and he take the 14 minute course in C++.After he graduates ( 3rd in his class ) he fires up his new C++ compiler and simulates a billion coin toss games. He walks up to our distinguished panel and says, " Do you guys know that the chance of getting 5 tails before you get 3 heads is 1 / 4?"

A says) Hmmm, I will have to think about that for a couple of years.

2 years later:

I got it: Let g be a group and G be a metric. If h(x) is meromorphic to... 5000 lines later. You are right D!

B says) After trying to read the 5000 lines, "That is not right. I do not know about that meromorphic jazz but the correct probability is 7 / 38."

C says) B, it is definitely 1 / 256. You just multiply ( 1 / 32 ) by ( 1 / 8 ).

D says) My code is correct. It is 1 / 4 =.25

E says) Are you sure of that 2, after all it is an approximation of an approximation. That 2 could be 1.98.


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.

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#623 2011-03-06 23:30:57

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi bobbym,


"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

#624 2011-03-06 23:48:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: What do you think?

Hi gAr;



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.

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#625 2011-03-06 23:57:28

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: What do you think?

Hi,

No problem.
What do you think of my approach?
Is there a solution given in the source?


"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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