Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

Hi Bobby,

Not close.

Is

close?*Last edited by phrontister (2010-01-22 04:59:38)*

"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

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

bobbym wrote:

Prove that:

Are you sure the equation is correct, Bobby? I tried s=7, and that ended up way off.

But I probably don't understand the question.

"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

Offline

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

It only works when |s| < 1. Otherwise the right hand side doesn't converge.

Why did the vector cross the road?

It wanted to be normal.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi phrontister;

You are closer, but more than 200 away. As for the series, yes as mathysyperson points out. (-1,1) is the interval of convergence.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

bobbym wrote:

You are closer, but more than 200 away.

How about

?"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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi phrontister;

Closer but still a ways off.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

Grumble!

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

Hope

is the closest yet!*Last edited by phrontister (2010-01-22 16:37:05)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi;

That is the closest yet, but not dangerously close.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi;

Problem #18:

Find n which is greater than 1, so that the average of

is a perfect square. Can you get a general solution?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

bobbym wrote:

That is the closest yet, but not dangerously close.

I'm beginning to feel dangerous...I think!

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi phrontister;

That is closer, but...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

A tough one;

Problem #19:

Two random numbers a,b are drawn from (0,1) and added to form c.

a + b = c.

a,b,c are then rounded to the nearest integer and called A,B,C respectively.

What is the probabilty that A + B = C?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

bobbym wrote:

That is closer, but...

Is

getting warmer, Bobby?Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi phrontister;

Bingo, 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.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

bobbym wrote:

Bingo, good work!

How did you do it, Bobby?

My first attempt was For/Next loops in BASIC (the only programming language I know a little about), but I kept on overlooking something. Then I saw that I could solve the puzzle in Excel, but I didn't think and threw my BASIC work away...and now I wish I hadn't.

I wondered also if it could somehow be done with permutations, but I know nothing about that subject.

My spreadsheet

*EDIT:* There was a typo in my spreadsheet formulas...now corrected. Sorry!

*Last edited by phrontister (2010-02-01 11:14:36)*

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

Hi Bobby,

I don't know if you've tried my spreadsheet formulas, but I made a typo yesterday. I corrected it just a few minutes ago. Sorry 'bout that, if you've wasted some time on it!

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi phrontister;

Not yet, I have been trying to reconstruct my solution.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi

Problem #20:

This one is easy:

An owl is perched on the top of a pole which is 9 ft high.. A gopher, 27 ft away is making a mad dash to its hole at the base of the pole. The owl pounces on the gopher. If their velocities are the same what distance from his hole is the gopher caught?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

Hi Bobby,

The gopher is caught 12 feet short of his hole.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi phrontister;

That's correct! Do you have an interesting method of solution? Hide it when you post it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

Hi Bobby,

Do you have an interesting method of solution?

Not really...

is what I did.*Last edited by phrontister (2010-01-31 23:12:20)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Hi phrontister;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,352

Hi Bobby,

Yes...that's a very nice, logical answer. Done the proper way, I think.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,908

Actually, nothing proper about it at all. Your method using interval bisection is what I wanted to use, I was quite unhappy when I found there was an algebraic way to do it. On another forum a bunch of academicians are pounding my type for finding other ways to do things. I am heavily outnumbered over there and in a rebellious frame of mind so I would have loved to have used your method.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline