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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Nice problem, btw. I enjoyed 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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Yes, it was tricky to solve mathematically too. You did show me a trick or two with your use of geogebra. Thanks for working on the problem.

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

I made a start on a mathematical solution to see if I could get to your 100 decimal-digit solution, but after struggling with it for a fair bit I let it go and solved it with Geogebra in a flash. So easy to use for something like this!

A very clever program, and I particularly like the great accuracy you can get with points etc that come alive when your mouse comes within cooee of them so that mouse clicks don't have to be pixel-perfect.

I found the area of the EFGH poly mathematically to umpteen decimal places:

I couldn't work out how to calculate segment areas to the same umpteen decimal places as the poly, and as it was getting too late I let it go and took the Geogebra road instead. When I'm more awake I might try again for the mathematical solution.

*Last edited by phrontister (2012-09-25 05:38:35)*

"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: 87,247

Hi phrontister;

The solution I did was very tedious but it only requires some formulas and attention to detail. Let me know if you need some of it.

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

My poly area solution was also quite tedious. I had no idea as to how to find the area of an irregular polygon and so I googled it. I don't remember the method exactly now, but I think it used Heron's Formula and I added the two triangles together to get the answer in my previous post.

I'll sing out for help if I try the maths solution and get stuck. Thanks!

Bed nowzzzz.

"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: 87,247

Hi;

You did the right thing. Google is your friend. It was how I got mine too.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

phrontister wrote:

Hi Bobby,

My poly area solution was also quite tedious. I had no idea as to how to find the area of an irregular polygon and so I googled it. I don't remember the method exactly now, but I think it used Heron's Formula and I added the two triangles together to get the answer in my previous post.

I'll sing out for help if I try the maths solution and get stuck. Thanks!

Bed nowzzzz.

Hi phro

Maybe it was the shoelace method?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

I sure would like to see you duplicate my answer with one of your own.

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 stefy,

'shoelace method': "A technique for lifting oneself off the ground by pulling on one's own shoelaces, which, when mastered and applied properly, will guarantee a 100% failure rate."

No, I didn't use the shoelace method...I'm quite sure it was Heron's Formula because although I didn't keep my notes I recall some of the steps I used, and they're the same. I'd given up on the problem until I thought of using Geogebra.

I suppose I must have used an angle measurement from my Geogebra drawing as I think it's necessary for an area calculation of an irregular polygon.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

I suppose I must have used an angle measurement from my Geogebra drawing as I think it's necessary for an area calculation of an irregular polygon.

There is a formula for that too.

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,

I'll see if I can find that formula.

I used too many steps in Geogebra to get to the result, and so I've revised it (see image).

Off to work now...

*Last edited by phrontister (2012-09-26 22:16:16)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

Very good! The formula for any polygon can be done with M using determinants.

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,

Just found out you can link any spreadsheet cell to text in the Graphics view via the pull-down menu on the Objects button in the text box's popup window. Excellent! That means all text and numbers in the Graphics view and the spreadsheet of my project are now linked dynamically.

The formula for any polygon can be done with M using determinants.

Hmmm. This is all I know about determinants.

And this is what I know about matrices. Maybe the numeric content is somehow related to something, but I've yet to reach a conclusion about that.

I think I'll just stay with the Geogebra solution, Bobby. Time's a bit tight for me right now, anyway.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi phrontister;

Okay, but if you ever need to do it to very high precision. Higher than geogebra, then M can do it for you.

Very nice vid!

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: 87,247

**New Problem:**

**E is confronted with this problem on the job.**

**http://www.mathsisfun.com/puzzles/extra … ution.html**

**Her boss asks her to verify B's solution.**

**http://www.mathisfunforum.com/viewtopic … 04#p234004**

**A has argued with the boss that B's solution is not correct. A says there is another solution. The boss is not sure, he asks B, who says there is only one solution and he can prove it. The boss asks E to verify B's solution without using a computer program. She can use Alpha but he wants a math solution. Can you help E prove B is right?**

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Isn't the pair of equations from the other thread enough?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Not for the boss and A. The boss knows that if there was another solution then those equations have to be wrong.

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: 87,247

**New problem:**

**A die is rolled 3 times. What is the probability that the maximum value of the faces is 3?**

**A says) Man, that is so easy. I hardly even broke a sweat doing it. My probability must be getting better!**

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Are the dice different?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

One die is rolled 3 times.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Oh, okay then.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

I have a feeling about what might be the next Baffler.

I will try coding a solution.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

You got it!

**New problem:**

**A die is rolled 20 times. What is the probability that the maximum value of the faces is 3?**

**A says) I still think it is:**

**What is you answer?**

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

I knew it!

This one is tougher...

Here lies the reader who will never open this book. He is forever dead.

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