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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: 92,264

No problem.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,264

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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: 92,264

Hi Jane;

Correct! Good answer!

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,264

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.**

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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: 92,264

Yep! Good job!

**In mathematics, you don't understand things. You just get used to them.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,264

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.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,960

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: 92,264

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.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,960

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: 92,264

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.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,960

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: 3,960

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: 92,264

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.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,960

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: 92,264

Not close.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,960

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: 3,960

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: 92,264

Yes, you have the constraints right.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,960

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: 92,264

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.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,960

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,264

Here is an easy one:

Problem #17:

Prove that:

**In mathematics, you don't understand things. You just get used to them.**

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