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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,233

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,233

**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.**

**Online**

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Wondered what Kubeiagenesis meant, and someone has explained in amazon site.

The book's very good!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,233

It was only in one library here for a long time so I never knew the correct title.

I stumbled upon it yesterday and I was very glad.

**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,233

**New Problem:**

**What is the smallest number that has a digital sum of 128?**

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: 3,845

Is it 299999999999999?

"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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Hi phrontister

That was also my first guess.

Another thing that pops into my mind is we have to find the smallest number whose digital sum is 128 in some base, but not necessarily decimal...

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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

Hi stefy,

Yes, I thought of that too, but I'm not too clued-up on bases and let that slide. I also wondered about it being a negative number, but let that go too because I thought that 'smaller than' wasn't necessarily 'less than' when referring to a number. Mathematica gives 128 as the digit sum for the positive and negative versions of my 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: 3,845

This answer is pretty small (4-pixel high numbers + 1-pixel borders). I would have liked to have gone smaller but stopped there because I don't know how to form numbers properly that are less than 4 pixels high; and besides, my old CRT monitor probably wouldn't be able to display sizes lower than that clearly enough to be able to make out the figures.

*Last edited by phrontister (2013-09-30 15:45:29)*

"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: 3,845

Here is a pdf file with a very tiny display of my answer in the top left-hand corner of the page. You'll need to zoom in to see it. It's the smallest answer I can come up with so far.

Below is an image of the pdf page at 100%. If you look closely you'll see a faint splotch in the top left-hand corner, that, because it's a graphic of the tiny font, is just a blur at any magnification. The only way you'll be able to read the answer is by zooming in on the actual pdf page with its magnifiable font. My pdf reader (PDF-XChange Viewer) has up to 6400% zoom (as do Nitro and Adobe) and displays the tiny print at a very readable size.

*Last edited by phrontister (2013-10-01 03:23:09)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,233

Hi;

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: 3,845

Hi Bobby,

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,233

Hi;

That was the tiniest answer I have ever seen or not seen.

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: 3,845

But you at least saw the splotch?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Hi phro

Copy/pasting the small text works miracles!

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: 86,233

The splotch? Oh yes I did see that. Spilled some soup on my monitor and it looked like a giant amoeba was eating the forum.

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: 3,845

Hi stefy,

You mean the small text in the pdf from post #1162?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Yeah, the one.

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: 86,233

Did you get the answer too?

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: 15,518

Hi

I am getting the number with one 9 less than the number in his PDF... 299999999999999.

*Last edited by anonimnystefy (2013-10-01 03:38:21)*

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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

The good retention of the font crispness through the magnification range I tried on it (6400% in any of the 3 pdf viewers I mentioned above) amazed me. Which program did you paste it into?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,233

I did not think of that. A hearty congratulations for getting the right answer.

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: 3,845

Oops! One too many nines in my pdf. I meant to have 14 of them.

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