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

Hi Bobby,

Not close.

Is

close?*Last edited by phrontister (2010-01-22 04:59:38)*

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

bobbym wrote:

Prove that:

Are you sure the equation is correct, Bobby? I tried s=7, and that ended up way off.

But I probably don't understand the question.

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

It only works when |s| < 1. Otherwise the right hand side doesn't converge.

Why did the vector cross the road?

It wanted to be normal.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi phrontister;

You are closer, but more than 200 away. As for the series, yes as mathysyperson points out. (-1,1) is the interval of convergence.

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

bobbym wrote:

You are closer, but more than 200 away.

How about

?"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi phrontister;

Closer but still a ways off.

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

Grumble!

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

Hope

is the closest yet!*Last edited by phrontister (2010-01-22 16:37:05)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi;

That is the closest yet, but not dangerously close.

**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi;

Problem #18:

Find n which is greater than 1, so that the average of

is a perfect square. Can you get a general solution?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

bobbym wrote:

That is the closest yet, but not dangerously close.

I'm beginning to feel dangerous...I think!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi phrontister;

That is closer, but...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

A tough one;

Problem #19:

Two random numbers a,b are drawn from (0,1) and added to form c.

a + b = c.

a,b,c are then rounded to the nearest integer and called A,B,C respectively.

What is the probabilty that A + B = C?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

bobbym wrote:

That is closer, but...

Is

getting warmer, Bobby?Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi phrontister;

Bingo, good work!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

bobbym wrote:

Bingo, good work!

How did you do it, Bobby?

My first attempt was For/Next loops in BASIC (the only programming language I know a little about), but I kept on overlooking something. Then I saw that I could solve the puzzle in Excel, but I didn't think and threw my BASIC work away...and now I wish I hadn't.

I wondered also if it could somehow be done with permutations, but I know nothing about that subject.

My spreadsheet

*EDIT:* There was a typo in my spreadsheet formulas...now corrected. Sorry!

*Last edited by phrontister (2010-02-01 11:14:36)*

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

Hi Bobby,

I don't know if you've tried my spreadsheet formulas, but I made a typo yesterday. I corrected it just a few minutes ago. Sorry 'bout that, if you've wasted some time on it!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi phrontister;

Not yet, I have been trying to reconstruct my solution.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi

Problem #20:

This one is easy:

An owl is perched on the top of a pole which is 9 ft high.. A gopher, 27 ft away is making a mad dash to its hole at the base of the pole. The owl pounces on the gopher. If their velocities are the same what distance from his hole is the gopher caught?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

Hi Bobby,

The gopher is caught 12 feet short of his hole.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi phrontister;

That's correct! Do you have an interesting method of solution? Hide it when you post it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

Hi Bobby,

Do you have an interesting method of solution?

Not really...

is what I did.*Last edited by phrontister (2010-01-31 23:12:20)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Hi phrontister;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

Hi Bobby,

Yes...that's a very nice, logical answer. Done the proper way, I think.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,436

Actually, nothing proper about it at all. Your method using interval bisection is what I wanted to use, I was quite unhappy when I found there was an algebraic way to do it. On another forum a bunch of academicians are pounding my type for finding other ways to do things. I am heavily outnumbered over there and in a rebellious frame of mind so I would have loved to have used your method.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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