What do you think?

gAr · 2011-02-23 23:04:35

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.

bobbym · 2011-02-23 23:21:31

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.

gAr · 2011-02-23 23:28:03

Yes, I saw that it overcounted. Got your first answer.
Anyway, a very good problem, thanks!

bobbym · 2011-02-23 23:34:23

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.

gAr · 2011-02-23 23:44:22

Thank you!

gAr · 2011-02-26 01:00:17

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)

bobbym · 2011-02-26 01:19:53

Hi gAr;

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

gAr · 2011-02-26 01:35:49

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!

bobbym · 2011-02-26 01:40:06

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.

gAr · 2011-02-26 01:49:30

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

bobbym · 2011-02-28 01:19:58

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!

gAr · 2011-02-28 05:36:19

Hi bobbym,

I assume you mean the sum of the consecutive squares.

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

bobbym · 2011-02-28 05:39:30

Hi gAr;

gAr · 2011-02-28 05:44:39

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

bobbym · 2011-02-28 05:54:37

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!

gAr · 2011-02-28 22:13:56

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)

bobbym · 2011-02-28 22:30:06

Hi gAr;

gAr · 2011-02-28 22:40:25

Oh, I see.

phrontister · 2011-03-01 01:59:38

Hi Bobby,

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

Howardroark · 2011-03-01 05:48:08

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!

bobbym · 2011-03-01 13:37:29

Hi Howardroark;

Hi phrontister;

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

bobbym · 2011-03-06 06:29:38

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.

gAr · 2011-03-06 23:30:57

Hi bobbym,

bobbym · 2011-03-06 23:48:38

Hi gAr;

gAr · 2011-03-06 23:57:28

Hi,

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

Math Is Fun Forum

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

Re: What do you think?

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