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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Hi Fruityloop;

How are you doing?

The proof is correct but it does use some calculus in the form of a Taylor expansion of e^(x+1).

But because it is you it is okay with me! Good work!

**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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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 120

You know what? After I posted I realized my solution doesn't conform to the conditions of the problem.

posted by Bobbym wrote:

But because it is you it is okay with me! Good work!

You are too kind!

*Last edited by Fruityloop (2010-10-15 17:40:31)*

The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Hi Fruityloop;

I am not kind I am vicious. Or at least I am kind of vicious.

**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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**jimmyR****Member**- Registered: 2009-05-29
- Posts: 143

Hi bobbym;

She is on a roll.

Elaina wrote:

Hi bobbym;

First, I need to say congratulations on you second small publication on the (deleted).

Eric spotted it and said he was impressed. He said you were always the best in his mind.I don't understand your reluctance to publish more. Jimmy told me you have nine or ten more like that.

Need I remind you that scientific work is to be shared.I haven't moved in your complex yet and may require your help in doing so.

*Last edited by jimmyR (2010-10-21 20:03:07)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Hi Elaina;

You are correct for problem #147

You are also correct on problem #149 , nice use of Napiers identity.

Elaina wrote:

First, I need to say congratulations on you second small publication on the (deleted).

Thanks, but kindly refrain from mentioning details of my private life.

Elaina wrote:

Eric spotted it and said he was impressed. He said you were always the best in his mind.

Well, there you have it, I always said he was out of his mind and now I have evidence.

The men in the white coats will soon relieve his dementia.

Elaina wrote:

I don't understand your reluctance to publish more. Jimmy told me you have nine or ten more like that.

Need I remind you that scientific work is to be shared.

Just because you cannot understand something does not make it a viable alternative for me.JimmyR is correct but what of it.

I do not feel that the remaining ones are so important that the "scientific community" cannot do without them.

When I think something is interesting I will gladly publish it there, not before.

I do not need reminders from you.

**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: 87,256

Hi 123ronnie321;

What did you get for the roots of x^3 -8x - 8 = 0 ?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

Hi bobby,

sorry,

The roots of above equation are **real** and are -2, 1 + sqrrtt(5), 1 - sqrrtt(5).

and they do satisfy the conditions of the problem.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Hi 123ronnie321;

Then you have solved the problem! Congratulations, that is the correct answer.

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: 87,256

Are there any integers that are perfect squares and when you reverse the digits are also a perfect square?

A says) I know everything about the integers, of course and there are an infinite amount of them.

B says) I am not so sure, at present I really do not know, but I doubt it.

C says) Yes! Here is a clue, the digits are 986 _ _ _ _ _ 36. You guess the middle 5.

D says) Whatever B says I disagree with. If he doubts it, there must be zillions of them.

A says) Here! Here!

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: 3,848

Hi Bobby,

Re perfect squares and their reverse...

"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: 87,256

Hi phrontister;

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: 87,256

The elements of a sequence are bracketed like this:

(1)

(4,10,20)

(35,56,84,120,165,220)

(286,..........10 elements)

(.......15 elements.....)

Find the 3000 th number and in which bracket it appears. For instance the 7th number is 84 and it is in the third bracket.

A says) Impossible, for once I say you need a blasted computer.

B says) It is not too difficult, I have the answer.

C says) What are sequences?

Who is right? If you pick B you are going to have to find the number and the bracket it is in.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Hi gAr;

Correct! That is very good!

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Thanks bobbym,

Nice problem on tetrahedral numbers...

"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Hi gAr;

Only 2 people solved it on 2 forums! That is odd.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

There may be people who know and choose not to post the same solution again. They may post a solution if they find another way of solving 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."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Each school in the city sent a team of 3 students to a mathematics contest. A, B and C were on the same team. Each participant in the contest received a different score. A's score was the median among all students, and his was the highest score on his team. B placed 37 and C placed 64th.

A says) There was 32 teams in the contest.

B says) That is not how many there were, it was less than that.

C says) B is right that is not right, I counted them and it was 30 teams.

A says)No wonder I scored the highest.

How many teams were sent?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Yeparoo! Very good! How did you figure it?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

Good! I like it.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

thank you:)

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,256

A man wants to get from A to B. He wants to make only up and right moves. Obviously going left or down are wastes of time.

A says) There are 540 ways to go from A to B.

B says) I do not know.

C says) Why do people want to move around?

D says) A is wrong but I cannot prove it.

Can you prove A is wrong by finding out the number of paths? The red grid lines are the streets.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

*Last edited by gAr (2011-01-18 14:44:37)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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