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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

Hi Bobby,

Thanks for your explanation...I even made sense of most of it!

I had to ignore "methods of interpolation" and "I curve fit that table", because they went over my head.

We had the same major goals, but went about it a little differently.

Here's a better explanation of my method.

*Last edited by phrontister (2010-05-11 02:40:37)*

"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****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

Thanks, for providing it. I actually got a little of it. Thanks also for the music. What happened to you at metamorphosis?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

bobbym wrote:

What happened to you at metamorphosis?

Work's been very hectic these past few weeks and I just can't fit everything in. Something out of maths problems and word games had to give, and the extra variety in maths has been the drawcard.

I enjoy word games, and metamorphosis is a good challenge. Must get back into it again...when I can.

Thanks for letting me know...I'd forgotten about it.

"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****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

Also your challenge has been solved over at club 13. Will you check the solution and verify it's uniqueness.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

bobbym wrote:

Also your challenge has been solved over at club 13. Will you check the solution and verify it's uniqueness.

Done!

"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: 4,593

Hi Bobby,

I guess I could just substitute for n to get one formula, which avoids having to do any plugging in.

*Last edited by phrontister (2010-05-11 14:18:35)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

bobbym wrote:

Thanks also for the music.

That was something I did to help one of my relatives with their school project on synthesizers, as an example for how synths can be used to bring a variety of sounds into a performance.

The quantizing feature was very helpful!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Thanks again for your new solution! Good work!

Did you ever want to be a musician, or something like that?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

I was always far too sports-mad (tennis, table tennis, Aussie Rules football, squash) to be interested in learning to play a musical instrument - which disappointed my mother greatly (she played the guitar and sang beautifully).

For a while I got a bit of an interest going in playing the synth, but after I'd tried out all the buttons that interest evaporated.

I like unaccompanied voice harmonies and sing in an a cappella male quartet. That takes up a lot of my time as I lead the group.

I prepare sheet music for the others on a midi-compatible software program, and burn a CD for each of them with their part in the right channel and the other 3 parts in the left...to help with learning their part. For the sounds I use a midi tone generator that the sheet music program can talk to.

We're just an amateur group and sing at our church camps and conventions, and sometimes at weddings. Good fun!

*Last edited by phrontister (2010-05-11 14:25:25)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

So you are a singer too. You are man of many talents. Glad to know ya!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

bobbym wrote:

Glad to know ya!

The pleasure is mine. I enjoy your input and helpfulness.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Prob 51

here is a super easy one. What is the sum of all the coefficients of

(1 + x - x^2)^20000

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

Hi Bobby,

Had to look up MIF's definition of *coefficient*, as I'd either forgotten it or wasn't taught it. The former is the more likely!

I think the answer is

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

Here is how to cheat and get some indication of what the answer might be,

It is not as large a problem as I thought. It appears that there are only 40001 terms in that expansion. Large but certainly possible.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

Hi Bobby,

Thanks for your explanation. Looks like the answer probably is

.*Last edited by phrontister (2010-05-11 17:53:41)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

That is correct reasoning, normally after playing spot the pattern you would use some proof technique like induction to prove your guess is correct. But for problems, no one ever does...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,593

Ok. Had to look up *induction *now (Wikipedia, as it's not on MIF). You keep on sending me to the dictionary! Just a quick look only, but I sort of get a rough idea about it. Way beyond me at my unlearned stage.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Woops, you did it, I feel a rant coming on. Yep!

Rant: Induction a tedious technique that no one ever uses on a forum. I have seen hundreds of posters say to another poster, use induction. But I have never seen them actually use it. The AOPS is huge on recommending induction. After searching through 40000 posts I couldn't find a single example of someone going through the actual process. Today, over there, someone actually proved something using induction. To my knowledge I am one of only 2 humans who has ever used induction to prove a recurrence on a forum.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

A nice problem that is pretty easy. Maybe you can inprove on my ugly solution:

Prob 52

Jack walks up a steep hill and back. He spends spent 80% of the time walking uphill and 20% of his time returning downhill. He averaged 3 miles per hour uphill, what is his average speed for the total trip?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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

Why did the vector cross the road?

It wanted to be normal.

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

mathsyperson wrote:

is it any better??

If two or more thoughts intersect, there has to be a point!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

mathsyperson and ZHero;

Both answers are correct! Good work!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Prob 53

Two die are thrown at once. The sample space is 2,3,4,5,6,7,8,9,10,11,12. How many times must this be done on average to get all eleven numbers?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Prob 54

A bunch of quarters, dimes , nickels and pennies has an average value of 14 cents. If a quarter is replaced by 25 pennies the average would drop to 7 cents. Or if a nickel was replaced by 5 pennies the average becomes 12 cents. What is the largest amount of nickels you can have?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Prob 55

Can you solve this?

HURRAH + HURRAY = PUZZLES

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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