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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: 106,390

No problem.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,390

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,390

Hi Jane;

Correct! Good answer!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,390

Hi;

Problem #14:

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,390

Yep! Good job!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,390

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!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,452

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: 106,390

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?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,452

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: 106,390

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,452

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: 4,452

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: 106,390

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,452

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: 106,390

Not close.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,452

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: 4,452

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: 106,390

Yes, you have the constraints right.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,452

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: 106,390

Hi;

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,452

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,390

Here is an easy one:

Problem #17:

Prove that:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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