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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Hi

Did you try W.A.

Solve[x^3 + 1/x^3 == 52,x]

Keep hitting more digits even though you will see the exact answer there too. I didn't use this idea because I found one that gives a general solution for any power. I will post it soon, in the original post.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

bobbym wrote:

Did you try W.A.

No I didn't. I only 'know' the tiniest bit of Mathematica...which only came about because of some correspondence I had with the person who solved my YOB puzzle by using Mathematica. I dabbled with M. a bit initially but thought it was too complex a program for a mere dabbler like me.

I put your formula into W.A. and had a quick look at the results. Have to go to work now, so a better look will have to wait until tonight.

"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: 105,251

Forgot the x at the end of the command, so I edited post #176. Have a good day at work.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

Hi Bobby,

I entered "Solve x^3 + 1/x^3 = 52 for x" into W|A, and its interpreter got my drift. That's an excellent feature for novices like me!

It gave out the formula you posted, so if I'd used W|A instead of Excel I might have avoided that inaccuracy problem.

I didn't use this idea because I found one that gives a general solution for any power.

Mine does too (I think), now that I've got rid of that approximation.

Thanks for your well-wishes, but I had a rotten day at work. Someone muffed it, which wrecked my plans...and so I got next-to-nothing done. I should have stayed home and enjoyed myself on MIF...which also gets next-to-nothing 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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

This one is really, really easy.

Prob #39

100 men can complete a job in 19 days. They work at a steady pace. After 13 days 11 men leave, how long does it take the remaining guys to finish the job? Justify and hide your answer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

Hi Bobby,

My answer assumes that there isn't a work-capacity imbalance in the workers of the two groups: such as, for example, that which is in 'Dilbert's Salary Theorem' and my disproof to it (see image).

*EDIT: Ignore the second image. I replaced it with the first one, but that second one won't delete.*

*Last edited by phrontister (2010-04-12 02:16:41)*

"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: 105,251

Hi;

That answer is correct. Good work!

Yes, I just got it now. Dilbert's theorem? I never thought of it that way. It actually makes sense to me.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

bobbym wrote:

It actually makes sense to me.

Likewise. It makes perfect ¢¢ to me too.

Mine was just a totally-tongue-in-cheek disproof of a well-established, real-life factual theorem.

*Last edited by phrontister (2010-04-12 01:23:05)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Did you write it?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

Yes...I wrote the disproof. 'Twas just a bit of fun with a friend of mine, who emailed me the theorem, claiming "Can this theorem be disproved??? I don't think so!!!".

I couldn't resist the challenge!

It went on from there. My disproof was 'Reproved', which I then followed up with 'Unreprooved' (the last of them).

*Last edited by phrontister (2010-04-12 01:24:05)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Well written and good! Actually the comments you made in the last paragraph have been my feelings for a long time. Does anyone still know who BB is? It was required reading in my time and one of my favorite books.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

Hi Bobby,

Does anyone still know who BB is?

I can't admit to 'still' knowing anything about that (not that I ever really did), because Tigeree says I'm 27.

I'll bore you with the last instalments of the massive missives about Dilbert's Salary Theorem's proofs etc. Here they are, in order from left to right.

Don't bother with them until you have absolutely *nothing *better to do!

*Last edited by phrontister (2010-04-12 03:21:39)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Hi phrontister;

Having read those incredible efforts. I have only this to say:

1) Mathematical Physicist... now you know why I hate those guys.

2) Squillions of years?

The whole shebang would not even been necessary had people listened to M's law.

BM wrote:

Work is a four letter word and should be outlawed.- circa 1975

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Okay, this one is baby easy.

Prob #40

If some polynomial is divided by ( x- 9 ) the remainder is 10. When it is divided by ( x+ 6 ) the remainder is 4. When it is divided by ( 3 x - 4 ) it has a remainder of 12. What is the polynomial?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

A new one:

Prob #41

Champernowne's number is defined as .123456789101112131415161718192021...

got the pattern, good. So 21 occurs at postion 32. Do not get confused by the 21 at position 14, it is not 21 but 12 followed by 13. At what position will 65536 occur?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

The alphametic

Prob #42

PUTINE + INOPURE +1432 + 2168 + YY = YYYYYYY

Has 2 solutions can you find them?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

Hi Bobby,

to Champernowne's number.

*Last edited by phrontister (2010-04-27 04:07:53)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Hi phrontister;

That's a really nice piece of work! Your answer is correct. Very good!!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Prob #43

A strange type of ball is dropped from 100 ft. On each bounce from the floor it does a strange thing. If the number of the bounce is a prime then the ball rebounds 4 / 5 of the height it fell from. If the number of the bounce is a composite number then it rebounds 3 / 5 of the height. How many feet does the ball travel before it comes to rest. To start you off:

The ball is dropped from 100 ft and hits the ground, since this is the first bounce and 1 is not a prime it rebounds 60 ft into the air. It falls again, 2 is a prime so it rebounds 48 ft into the air. So far it has travelled 100 + 60 + 60 + 48 = 268 ft.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

Hi Bobby,

The alphametic

.*Last edited by phrontister (2010-04-18 05:03:26)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Hi;

Correct! Nice solution.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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

bobbym wrote:

Hi;

Can you prove this using only algebra?

*Last edited by JaneFairfax (2010-04-18 05:54:22)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Hi Jane;

Sorry for the delay took me a while to verify your algebra. Correct!! Nicely done!

Here is the official answer:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,251

Hi;

Prob #44

Super easy:

Do this easy one and try to get it into this form:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,385

Hi Bobby,

*Last edited by phrontister (2010-04-25 03:05:02)*

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