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#1 2009-10-16 18:27:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

What do you think?

Hi;

1) Can you find an integer b such that:

is a cube?

2)

This one can be a little tough.

10 people attend a raffle. The probability that 4 people at the raffle have the number n is .2508. What is the probability that a random person at the raffle has that number.


3) A guy owns a small casino. It only has one gaming table. He would like to earn 1000 dollars a day with it. There is only a flat bet of 2 dollars per roll and the players probability of winning is 18 / 37. The payoff is 2 dollars. How many games must be played on average for him to earn his 1000 dollars. Since he doesn't like to lose he needs to also know what is his chance of losing in any single day.

There were certain inconsistencies in the way this problem was phrased originally, this created problems in solving it. These were pointed out by All_Is_Number. I have modified it to have a clean solution.

Last edited by bobbym (2009-12-02 08:12:01)


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.

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#2 2009-12-02 08:15:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hi;

This one is moderately hard.

Prob 3:

How many permutations of 3 letters can you make out of the word:

clandestine?


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.

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#3 2009-12-03 19:31:34

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: What do you think?

I thought about the first one for a while and couldn't conjure up an answer. Mind posting the results in hidden text?

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#4 2009-12-05 10:04:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hi;

Problem #4:

You can see 4 wire framed cubes stuck together and a spider at the upper left (A) and a fly at the bottom right,

How many paths can the hungry spider take to the immobilized fly? The spider is not a dummy. It always goes down and to the right (It can also take a diagonal). A to B, A to C and A to D are all legal. In short it always is crawling towards the fly. Also it must crawl along the wire edges of the 4 cubes.


Bonus: If there were 100 cubes stuck together instead of 4 and the fly was at the bottom right corner how many paths can the spider take?

Please hide your answers.

View Image: Spider.gif

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.

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#5 2009-12-06 16:10:11

Anakin
Member
Registered: 2009-10-04
Posts: 145

Re: What do you think?

Wow, that mod stuff is confusing. <.<

I'm gonna go Google it for a while and see if I come up with a result.

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#6 2009-12-07 11:28:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Here is a good one:

Problem #5:


You randomly choose 20 people. Find the probability that 5 of their birthdays are in the summer while 5 are in the winter. Of course all 4 seasons have the same number of months.


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

#7 2009-12-07 22:43:43

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: What do you think?


Why did the vector cross the road?
It wanted to be normal.

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#8 2009-12-08 04:39:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hi mathsyperson;

Correct!


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

#9 2009-12-13 09:30:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Problem #6:

12 guys began to eat a cake. They ate it in the following order:

Bob ate 8.2% of the cake.

Moe ate 5.1% of the remaining cake.

Larry ate 3.8% of the remaining cake.

Curly ate 3.5% of the remaining cake.

Shemp ate 2.3% of the remaining cake.

Bud ate 9.1% of the remaining cake.

Lou ate 5.0% of the remaining cake.

Groucho ate 6.2% of the remaining cake.

Chico ate 11.3% of the remaining cake.

Harpo ate 1.66% of the remaining cake.

Zeppo ate 3.2% of the remaining cake.

Last, Milton ate 7.8% of the remaining cake.

At the end the remaining cake weighed exactly 352 grams. How many grams of the cake did Moe eat? Round to the nearest whole gram.

Don't forget to hide your answer!


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

#10 2009-12-14 06:17:29

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,847

Re: What do you think?

Hi Bobby,

Last edited by phrontister (2009-12-14 06:30:26)


"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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#11 2009-12-14 07:18:58

Rasmushdahl
Member
Registered: 2009-12-10
Posts: 3

Re: What do you think?

Hi Bobby and everyone

I'am new to this forum :-)  My name is Rasmus and I come from Denmark. I would like to
post my answer, but i don't know how to hide it.

Rasmus

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#12 2009-12-14 07:45:36

Rasmushdahl
Member
Registered: 2009-12-10
Posts: 3

Re: What do you think?

I think I found out myself smile

Last edited by Rasmushdahl (2009-12-14 07:46:45)

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#13 2009-12-14 08:28:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hello Rasmus;

Welcome to the forum! Also, congratulations that is correct! Well done!


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

#14 2009-12-14 09:35:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hello phrontister;

I'm sorry I didn't see you up there. Very good! I knew you would get it.


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

#15 2009-12-14 22:54:39

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,847

Re: What do you think?

Hi Bobby,

I only saw your solution to #1 just now, so I'll stop my little brute force Excel spreadsheet program. I was getting close to melting my cpu, anyway!

I'd just passed 2,600,000 (had starting with zero) for the test value of b (no solutions, of course), and still had quite a way to go before reaching b's maximum test value of 18,257,418 (after that, 3b²+3b+7 comes to more than Excel's 15 digit max.)

I was too lazy to try to work out a better brute force option, but it would have gone the same way...nowhere.


"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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#16 2009-12-15 06:17:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hi phrontister;

Nothing wrong with that. Before I ever attempt to prove something I always let the computer try a couple of million examples, just to see if it might be true. Sometimes you find a counterexample for really small numbers.


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

#17 2009-12-23 11:50:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Problem #7:

Find all the whole number x's that when multiplied by 434782608695652173913 yield all nines.


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

#18 2009-12-23 12:02:20

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,847

Re: What do you think?

bobbym wrote:

Find all the x's that when multiplied by 434782608695652173913 yield all nines.

Found one so far:

Last edited by phrontister (2009-12-23 12:09:33)


"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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#19 2009-12-23 12:05:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hi phrontister;

That's one! You can leave out the decimal point.


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

#20 2009-12-23 12:12:48

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,847

Re: What do you think?

Oops! <blush> Corrected it.

Found two more:


"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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#21 2009-12-23 12:28:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Hi;

I am the one who should be blushing, I forgot to mention that x has to be a whole number. Am correcting the post. Sorry.


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

#22 2009-12-23 12:35:50

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,847

Re: What do you think?

Oh. I was just in the middle of typing out all the other decimal-place versions of that number when I saw your post.

Are there more answers than the one in my first post? I can't see how there could be.


"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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#23 2009-12-23 12:37:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,570

Re: What do you think?

Yes, there are an infinite amount of whole number answers. But they are very large.


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

#24 2009-12-23 12:53:40

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,847

Re: What do you think?

Are these the next two higher ones?

Yes...I can see that there are an infinite number of answers.

Last edited by phrontister (2009-12-23 13:01:15)


"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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#25 2009-12-23 12:58:36

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,847

Re: What do you think?

This is the largest answer my calculator can handle:

Used the copy/paste functions! And I didn't bother typing in the comma delimiters this time!

Last edited by phrontister (2009-12-23 13:40:03)


"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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