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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Yes, of course. should be 11.75. (9.75 is what both sides of the equation should be equal to.) Sorry, got confused.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

No problem.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

HI;

Problem #13:

From the set {A,B,C,D,F,G,H,I,J,K,L} , if the first 6th tuple is AAAAAA and the 10000th 6th tuple is {A,A,I,G,I,A} what is the millionth 6th tuple?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

*Last edited by JaneFairfax (2010-01-16 13:42:49)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Hi Jane;

Correct! Good answer!

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Hi;

Problem #14:

From the same set as in #53 what position does LHBICF occupy?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Yep! Good job!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Hi;

Problem #15:

What is the longest string of consecutive positive numbers that when added equal 2009?

Watch it it can be tricky.

This is the one I got. Is it the longest? No peeking!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

Hi Bobby,

I got the same as you, and did it like

*Last edited by phrontister (2010-01-19 04:41:38)*

"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Good! The question now is simple: Is there a problem that I can get that Jane or you can't get almost before I finish posting it?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

Hi Bobby,

Is there a problem that I can get that Jane or you can't get almost before I finish posting it?

For Jane, I think your only hope is to work out her sleep pattern and to post your puzzle just after she's gone to bed.

For me, just post anything that needs maths knowledge above year 4 high school level...but there's also a good chance that I've forgotten what I learnt up to that stage too.

*Last edited by phrontister (2010-01-19 22:40:22)*

"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: 82,980

OK, here is one that will stump ye!

Problem #16:

How many total integer solutions are there to the equations?

a + b + c + d + e + f = r

with r = 0,1,2,3,4,...60

f >= e >= d >= c >= b >= a >= 0

a,b,c,d,e,f < 11

Hint: It has been disguised to be difficult.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

Hi Bobby,

How many total integer solutions are there to the equations?

Is the answer

?"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: 3,819

Hey! Did you add "a,b,c,d,e,f < 11" later, Bobby? Maybe I missed seeing that... (I'll have to look at that later).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Hi phrontister;

Yes, I did, sorry for the confusion. I have also edited out the error you spotted. Thanks for pointing it out. I cleaned your quote up as well, otherwise it would have looked like you were talking about a phantom mistake.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

How close was my first answer? (Just wanna see if I'm on the right track)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Not close.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

Oops! Wonder where I went wrong. Back to the drawing board! (later)

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

bobbym wrote:

f >= e >= d >= c >= b >= a >= 0

Is ">=" the same as "≥"? That's what I took it to be.

Edit: And that:-

f ≥ e,

e ≥ d,

d ≥ c,

c ≥ b,

b ≥ a, and

a ≥ 0

a,b,c,d,e,f < 11

I take it that means that each of those letters is less than 11.

*Last edited by phrontister (2010-01-20 14:11:49)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Yes, you have the constraints right.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

bobbym wrote:

Not close.

Do you mean that it wasn't close to the answer to the original problem before that additional constraint?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Hi;

Without the constraint that they are all less than 11 the answer would be much larger, 241502 solutions.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,819

Yes...I just saw where I went wrong (overlooked 'some' options).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,980

Here is an easy one:

Problem #17:

Prove that:

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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