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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Theyre all wrong. Correct answer is

When *k* = −5 or 0, it still has 4 real roots (repeated roots count as two roots).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Good work Jane for pointing that out. I don't know how I missed that but I did. I chose d.

**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: 86,365

Hi;

Discussing the sum:

A says that n is divisible by 12347, B says n isn't divisible by 12347. Who is right?

**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: 86,365

Hi

How many integers from the set:

{5000, 5001, 5002, 5003, 5004, 5005, ... 10000}

are there that when you some the digits you get a sum of 21.

A says 123;

B says none

C says (10000 - 5000 -2) / 21

**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: 3,847

Hi Bobby,

I get

integers.*Last edited by phrontister (2010-03-06 19:36:17)*

"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: 86,365

Hi;

That looks correct, what did you notice about the answers that could have helped?

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: 3,847

Hi Bobby,

I didn't analyse the answers...I just did

.*Last edited by phrontister (2010-03-06 19:27:56)*

"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: 86,365

Good work! Thanks for the spreadsheet work.

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: 3,847

my code for the answer in BASIC.

How did you do it, Bobby?

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

Ah, I like your way. Nice and simple, write in under a minute, run in under a second.

Here's the overly complicated thing I'd have done:

Why did the vector cross the road?

It wanted to be normal.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

And I like what you've done, mathsyperson! Clever, efficient, with good insight and understanding that I lack. I puzzled over the fourth line but eventually saw what you did. Nice!

I don't know computing software such as MATLAB, but I wanted to see what your code did and installed FreeMat...where it ran fine. I converted your code to

, with this result: 0 milliseconds, compared with my 220ms if I don't print the list...only the total count.I also like using a spreadsheet for something like this, just for ease of analysing the result list and to play around some more with the figures.

*Last edited by phrontister (2010-03-07 11:55:27)*

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

Mine is more efficient, but 220ms is still virtually nothing and it probably took me a good while longer to write mine.

I tend to try making my code as optimal as I can even when it's not really necessary. Yours is probably a lot easier to debug too. (In fact, for a bit mine was giving a different answer to yours, and it took me a little while to figure out the reason)

Still, at least it's good practice for problems where efficiency can mean the difference between minutes and days.

By the way, thanks for mentioning FreeMat. I only had access to MATLAB while at University, and I've been looking for a good replacement for a while now.

Why did the vector cross the road?

It wanted to be normal.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Yes, the total time spent on my BASIC code was only a minute or two because of its simplicity.

The main reason I wrote it (I'd opted for spreadsheet initially to help analyse the results...and because I enjoy using Excel) was that I couldn't work out how FreeMat's debugger worked, and I wanted to see what your program was doing. BASIC's debugger revealed that very quickly...although, thinking about it more, I should have been able to understand it without turning to the debugger for help.

Learning all the time...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi

How many integers from the set:

{1^2, 2^2, 3^2, 4^2, ... 1 000 000 000^2}

are there that when you sum the digits you get a sum of 21.

A says 123000;

B says none

C says (1 000 000 000 - 500 000 000 -2) / 21

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Yeparooo! You have to admit it is a nasty question, especially after the other question.

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: 3,847

Yes, that *was *nasty...especially so soon after the other one as I was still stuck in that thinking mode.

I was unable to spot the logic that I knew had to be the key to the solution and so I peeked at mathsyperson's great answer. Until then I could only offer

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Yes, that was nasty...especially so soon after the other one as I was still stuck in that thinking mode.

You understand! When that problem was given to me it came after a long succession of problems that were of the first type. So I went along in a pavlovian way and succumbed to his sadistic trap.

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: 3,847

I only checked to 2,000,000^2, heading towards 1,000,000,000^2, but was fast approaching Excel's 15-digit limit...which I'd reach at 31,622,776^2. So I was beginning to scratch my head...

...his sadistic trap

That character sounds like he's the spitting image of a bobbym clone.

*Last edited by phrontister (2010-03-08 12:08:33)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

What is the remainder of 9 ^ 1995 when divided by 7?

Who is right?

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: 3,847

Hi Bobby,

I did

.I had a look at your answers but was in too much of a hurry and didn't understand them. I'll have a better look at them later...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

H phrontister;

What program did you use?

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: 3,847

I used BCalc, a freeware scientific calculator.

I also checked my answer with WolframAlpha...which automatically changed my 'int' function to the 'floor' function.

*Last edited by phrontister (2010-03-10 09:14:23)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

If

Then what is 1 / x^4;

Is A right?

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: 3,847

Hi Bobby,

I think that A is

.*Last edited by phrontister (2010-03-14 11:45:03)*

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