[Neraphym]

I'm going to post a few hard math questions. I will weigh each question based on its difficulty and award points to the first person to give me a right answer. I dunno what the reward is going to be, since I don't play runescape anymore, but I'm sure I'll think of something.

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Question: 1
Rating: 4


You are a highway planner working for me. I need you to connect a bridge at point A to an interchange at point B. Point B is exactly 8 miles south and 8 miles east of point A. Here's the problem: there is a giant marsh in between the two. The marsh extends from west to east indefinitely and goes from the bridge to the south for 5 miles. Here is a picture:



It costs 10 million dollars per mile to build over marsh, but only 7 million dollars per mile to build on dry land. I need you to find the most cost-efficient value for building a road here (rounded to three decimal places).

Winner: Kaezion

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Question: 2
Rating: 2

Find the first number with 20 factors.

Winner: Bigrat2

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Question: 2
Rating: 3

What is the median number (middle value) and mean (average value) of all the prime numbers in the range of 1 to 10,000.

(In order for me to get the answer here, I'm going to have to write a program, and I can't do this on any of my home computers. You'll all have to wait until monday to see who's answer is right.)

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Scores:
Kaezion: 4
Bigrat2: 2

This post has been edited by Alpha Weapon: 14 May 2005 - 01:58 AM

[Serenarocks]

Are we just doing your homework? LOL

[Baseballl]

Could possibly be $100.410 million to go straight across.

$127 Million to go south from A, then east to B.

This post has been edited by Baseballl: 12 May 2005 - 10:55 PM

[Master Of Stuff]

Just want to say everyone is wrong... this job will be outsourced and done at $100k...

Seriousily: I think Base covered both cases. If he's wrong, then I might know an alternate answer.

[Baseballl]

Well, since the marsh isn't extended 4 miles, I'm assuming we might be able to go across with the info given... Hard to remember after not having this for 10 years. However, if you can't go across with the info given, then you can only go South, then East from A to get the cheapest cost.

[Mobster101]

ohh god what a fun thing...

[Hax the Cook]

I have a feeling you don't go straight south, but at a slight diagonal. I got 100.808 Million for straight south, but I'm sure you could get less.

[Baseballl]

Can go diagonal from B to the Dry/Marsh line, the north to A = $109.808 million

[Baseballl]

Official Answer: $99.127 million

[Kaezion]

My answer is $98.888 million.
I will post my work if you wish. I did, however, use a calculator to find the root of the derivative of the equation for total cost - as you know, this is necessary, as no human can find the zeros to that equation by hand.

EDIT: Just read the thing about 3 decimal places. So yeah, there it is.

This post has been edited by Kaezion: 13 May 2005 - 02:51 AM

[Neraphym]

Yep, its 98.888 million. I tried to get that derivative by hand... but I gave up and used the zero program. I'll post an easier one a bit later, but for now, Kaezion is winning with 4 points.

I put an really simple one up for some of the younger SeeDs.

And for the heck of it, I'll even give a free helper:

public class Divisors
{
public static void main(String[]args)
{
  int factors = 0;
  int test = 0;
  int x = 0;
  int l = 0;
 

  do
  {
  factors = 0;
  x = x + 1;

  for(int y = 1; y <= x; y++)
  {
    test = x % y;
 
    if(test == 0)
    factors = factors + 1;
  }

  }while(factors < 12);

  System.out.println(x);
}
}

This post has been edited by Alpha Weapon: 13 May 2005 - 02:15 PM

[Kaezion]

i need clarification on the second one. you mean, twenty factors, as in twenty distinct factors that are prime numbers? if that's what you meant, the answer is:
2*3*5*7*11*13*17*19*23*29*31*37*41*43*47*53*59*61*67*71 =
557940830126698960967415390.

[Neraphym]

No, that's not what I meant. Sorry for the unclrearlyness of the question.

[Ratty]

hehe, i remember doing this one aaages ago, was it 240?

[Neraphym]

Yup, 240 is the magic number!