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

That worked out a lot nicer than I expected (assuming I haven't stumbled somewhere)

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: 87,238

Hi mathsyperson;

That's correct!

Hi all;

Problem #31:

This one is so easy, I am tempted to do it.

A plane that can manage 500 mph in still air travels to a town 2000 miles away while the wind is blowing along the line of flight. If on the return trip the plane travels the same amount of time as going but still has 200 miles to go, What is the winds velocity?

**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,

TEN + TEN + NINE + EIGHT + THREE = FORTY

Are there multiple solutions to this? I get 7

*EDIT: I included my code (LibertyBASIC)*

*Last edited by phrontister (2010-02-28 13:36:03)*

"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: 87,238

Yes, very good that is correct!

**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: 87,238

Hi;

Prob #32:

Hard:

How many terms have coefficients that are divisible by 3 in the expansion of (a + b)^3000?

Prob #33:

Moderate:

An urn is filled with balls with value 1, 5 13, 23. There is an equal number of each. I pick 4 balls out of the urn with replacement. What is the chance that the sum of my 4 balls is < 25?

Prob #34:

Easy:

Candy goes into a store and spends 1 / 2 of her money + 10 dollars. She goes into the next store and spends 1 / 3 of her remaining money plus 12 dollars. Then she spends 1/4 of her remaining money + 9 dollars. If she is left with 17 dollars. How much did she start with?

**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,

*Last edited by phrontister (2010-03-14 03:04:22)*

"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: 87,238

That's correct.

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 used Excel's Goal Seek. I input a nominal $100 into B2, but in the image the cells display Goal Seek's output.

Were the $35 1/3 spent at store #2 and the $17 2/3 spent at store #3 i.o.u. transactions?

*Last edited by phrontister (2010-03-14 11:58:24)*

"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: 87,238

Hi phrontister;

I am not following you here.

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 am not following you here.

Re the i.o.u. reference?

Candy spent $35 plus 1/3 of a dollar at store #2 and $17 plus 2/3 of a dollar at store #3.

AFAIK, thirds of a dollar can't be made up from actual cold, hard, cash and so I guessed that there must have been some other means of payment. eg, an i.o.u.

*Last edited by phrontister (2010-03-14 14:10:36)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

I understand.

When i made up the problem, I actually got lucky solving a similar problem. I used the same erroneous method on this one and came up with the wrong answer but which always had whole numbers, for every step. Your answer made me check the method I was using. When I found the right way I realized the problem had problems. It was by accident that it had a whole number answer even at the end.

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,

Changing the problem to the following will yield a whole number at each step:

Candy goes into a store and spends 1/2 of her money + 8 dollars. She goes into the next store and spends 1/3 of her remaining money + 12 dollars. Then she spends 1/4 of her remaining money + 10 dollars. If she is left with 17 dollars, how much did she start with?

*Last edited by phrontister (2010-03-14 15:12:58)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi phrontister;

If I change it, the latter posts will be incorrect.

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: 87,238

Hi;

Prob #35

Can you prove this using only algebra?

Prob #36

This one is super easy, if you have been paying attention.

I flip a coin 15 times. How many ways are there with no 2 heads in a row?

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: 87,238

Hi;

This one you are on your own with. I borrowed it from another site.

Prob #37

Rationalize the denominator of:

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: 87,238

Hi;

This one is from another forum. I have modified it as it was too easy.

Prob #38

If x^3 + 1 / x^3 = 52 then what x^7 + 1 / x^7 equal?

Please don't check the other forum for an answer. Try it yourself and you will discover a better answer. Use the practical math maxim that it often easier to solve for a general solution than for a particular one. Otherwise I am just going to post more of these.

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 came up with

.I think my general solution gets the job done, but it's clunky.

*Last edited by phrontister (2010-04-08 21:14:24)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi phrontister;

That is an interesting idea. What do you get for your equation when y = 25?

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,

What do you get for your equation when y = 25?

And for other higher powers: inaccuracy.

I thought that might happen because of the approximation, and should have checked it out in WolframAlpha or my high-precision calculator first as they would have told me that in a flash...but I didn't think of it (rushing).

I had another idea in mind but didn't finish it. This one seemed to work - at least it did for the low powers - and so I posted it.

*Last edited by phrontister (2010-04-07 14:23:28)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Don't worry about it, I still think you are the coolest dude in Australia.

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

And Tigeree the coolest dudess in Australia.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

And Tigeree the coolest dudess in Australia.

Who?

Hi phrontister;

Okay, back to 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: 3,848

Hi Bobby,

That's a pretty big hint...nearly as big as the 'great big hint' that I gave to my NOHOW puzzle.

It works perfectly for all cases that I tried it on, but I've got no idea at all about the reasoning behind it (I tried). What are the steps for arriving at that formula?

I tested my improved general formula by using my calculator and WolframAlpha on various powers up to 636 - which is the highest W.A. will go to - and they agree on all.

But there are further improvements too? I'll need another hint!

*Last edited by phrontister (2010-04-08 03:22:11)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi phrontister;

It works perfectly for all cases that I tried it on, but I've got no idea at all about the reasoning behind it (I tried). What are the steps for arriving at that formula?

To answer your question partially, what techniques did you use to find your 3.73.... 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: 3,848

Hi Bobby,

...what techniques did you use to find your 3.73.... answer.

Nothing that involved much thinking or structure....Excel's Solver, set to high precision. I couldn't come up with a logical technique.

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