That was quick Philly! And yes the answer is right ;) Congratulations!

Question 66
Q66 Answer: 20th
Q66 Solver: Philly

Microsoft Windows Standings 2.0:
1. Fred W - 17 Points
2. William Rothamel - 16 Points
3. Guido.Man - 8 Points
4. Mr. Kevvy - 7 Points
5. Sarge - 5 1/2 Points
6. Dominique - 5 1/2 Points
7. WinterKnight - 5 Points
8. Philadelphia - 3 1/2 Points
9. John McLeod VII - 1 Point
10. Labbie - 1 Point
11. Scary Capitalist - 1/2 Point
12. TBD...

Philly quickly gaining speed going up the table....

Now for another question!

Q66 (1 Point) : A cloth bag contains a pool ball, which is known to be a solid ball. A second pool ball is chosen at random in such a way that it is equally likely to be a solid or a stripe ball. The ball is added to the bag, the bag is shaken, and a ball is drawn at random. This ball proves to be a solid. What is the probability that the ball remaining in the bag is also a solid?

Cya' all soon!
Luke.

50% since the second ball had a 50/50 chance, or "equally likely" of being chosen to be put into the bag. Since we know one of the balls is a solid for sure, the chance of the second being solid as well is 50%.

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Correct Again Philly! 1 Point to you!

Q68 Answer: 50% chance

Microsoft Windows Standings 3.0
1. Fred W - 17 Points
2. William Rothamel - 16 Points
3. Guido.Man - 8 Points
4. Mr. Kevvy - 7 Points
5. Dominique - 6 Points
6. Sarge - 5 1/2 Points
7. WinterKnight - 5 Points
8. Philadelphia - 4 1/2 Points
9. John McLeod VII - 1 Point
10. Labbie - 1 Point
11. Scary Capitalist - 1/2 Point
12. TBD...

Q69 (1 Point) : Is the number 2,438,100,000,001 prime or composite? No calculators or computers allowed!

Luke.

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- Luke.

Any Answers?


Q69 (1 Point) : Is the number 2,438,100,000,001 prime or composite? No calculators or computers allowed!

Luke.

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- Luke.

Any Answers?


Q69 (1 Point) : Is the number 2,438,100,000,001 prime or composite? No calculators or computers allowed!

Luke.

Q69: It is prime.
(And if I am wrong, the next poster gets the point?)

F.

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Any Answers?


Q69 (1 Point) : Is the number 2,438,100,000,001 prime or composite? No calculators or computers allowed!

Luke.

As 2,438,100,000,001 is 300^5 + 300^4 + 1, I would say it has to be composite.

With such a large number it would be a long slog to even try the various tests for primality. Using Euclid's sieve would take me the rest of my life.

I would would have to cheat by writing a nifty program. Some of the tests only find certain types of primes and and involve Galois sets and other forms of set theory--they are also computationally intensive and i would have to use a calculator anyhow to keep from making an arithmetic error.

I thought that the long string of 100000001 looked like it would divide by nine--it looks like those numbers that you get when you repeatedly multiply by 999.... or other long sequences of 9's but I get a remainder of .1111111etc when I divide Luke's number by 9--- which is of course 1/9. Since this is a rational number I would guess that the number is not prime.

With such a large number it would be a long slog to even try the various tests for primality. Using Euclid's sieve would take me the rest of my life.

I would would have to cheat by writing a nifty program. Some of the tests only find certain types of primes and and involve Galois sets and other forms of set theory--they are also computationally intensive and i would have to use a calculator anyhow to keep from making an arithmetic error.

I thought that the long string of 100000001 looked like it would divide by nine--it looks like those numbers that you get when you repeatedly multiply by 999.... or other long sequences of 9's but I get a remainder of .1111111etc when I divide Luke's number by 9--- which is of course 1/9. Since this is a rational number I would guess that the number is not prime.

I didn't try to divide by 9 since the sum of the digits is not divisible by 9 (same rule as for divisible by 3).

Then I ran out of steam and took a punt.

F.

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Any Answers?


Q69 (1 Point) : Is the number 2,438,100,000,001 prime or composite? No calculators or computers allowed!

Luke.

2438100000001 = 73*33398630137

Not prime

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Ok, another big response.....

Q69 Answer: It's Composite

For this question:
I will award... WinterKnight ...1 point for achieving the correct answer first
But I will also give half points to... Bill, Dominique ...for also getting the correct answer. Sorry Fred, obviously you didn't get the right answer, but your still on top!

Microsoft Windows Standings 3.1
1. Fred W - 17 Points
2. William Rothamel - 16 1/2 Points
3. Guido.Man - 8 Points
4. Mr. Kevvy - 7 Points
5. Dominique - 6 1/2 Points
6. WinterKnight - 6 Points
7. Sarge - 5 1/2 Points
8. Philadelphia - 4 1/2 Points
9. John McLeod VII - 1 Point
10. Labbie - 1 Point
11. Scary Capitalist - 1/2 Point
12. TBD...

Here we go again:

Q70 : The towns of Alpha, Beta, and Gamma are equidistant from each other. If a car is three miles from Alpha and four miles from Beta, what is the maximum possible distance of the car from Gamma? Assume the land is flat.

Luke.

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- Luke.

Ok, another big response.....

Q69 Answer: It's Composite

For this question:
I will award... WinterKnight ...1 point for achieving the correct answer first
But I will also give half points to... Bill, Dominique ...for also getting the correct answer. Sorry Fred, obviously you didn't get the right answer, but your still on top!

Microsoft Windows Standings 3.1
1. Fred W - 17 Points
2. William Rothamel - 16 1/2 Points
3. Guido.Man - 8 Points
4. Mr. Kevvy - 7 Points
5. Dominique - 6 1/2 Points
6. WinterKnight - 6 Points
7. Sarge - 5 1/2 Points
8. Philadelphia - 4 1/2 Points
9. John McLeod VII - 1 Point
10. Labbie - 1 Point
11. Scary Capitalist - 1/2 Point
12. TBD...

Here we go again:

Q70 : The towns of Alpha, Beta, and Gamma are equidistant from each other. If a car is three miles from Alpha and four miles from Beta, what is the maximum possible distance of the car from Gamma? Assume the land is flat.

Luke.

7

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I make it be the square root of 34 which is 5.831 miles to 3 decimal places

Then again it could be the square root of 41 which is 6.403 miles

Well done Philly! Correct answer again! 1 Point to you...
Q70 Answer: 7

Microsoft Windows Standings 3.11
1. Fred W - 17 Points
2. William Rothamel - 16 1/2 Points
3. Guido.Man - 8 Points
4. Mr. Kevvy - 7 Points
5. Dominique - 6 1/2 Points
6. WinterKnight - 6 Points
7. Sarge - 5 1/2 Points
8. Philadelphia - 5 1/2 Points
9. John McLeod VII - 1 Point
10. Labbie - 1 Point
11. Scary Capitalist - 1/2 Point
12. TBD...

Question 71 (1 Point) : Create the best Pi approximation, e.g. 22/7, and show how many digits it is accurate to, you may refine your answer.

Luke.

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- Luke.

No Answers?

Question 71 (1 Point) : Create the best Pi approximation, e.g. 22/7, and show how many digits it is accurate to, you may refine your answer.

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- Luke.

No Answers?

Question 71 (1 Point) : Create the best Pi approximation, e.g. 22/7, and show how many digits it is accurate to, you may refine your answer.

Will 1,241,100,000,000 digits do?
but I'd need to borrow your PC.
Numerical Approximations of pi (Wiki): Modern Algorithms
"These approximations have so many digits that they are no longer of any practical use, except for testing new supercomputers."

or I'd alternatively use the Gauss-Legendre Algorithm, but it might just be easier to run Super-Pi ;D

The necessary taylor series expansions of the arctangent function shouldn't be too hard to devise, I already did it a while back for the sin function: http://spreadsheets.google.com/pub?key=pTEZyJrzS1aK2U0P2QioQaw

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"Living by the wisdom of computer science doesn't sound so bad after all. And unlike most advice, it's backed up by proofs." -- Algorithms to live by: The computer science of human decisions.

No Answers?

Question 71 (1 Point) : Create the best Pi approximation, e.g. 22/7, and show how many digits it is accurate to, you may refine your answer.

Will 1,241,100,000,000 digits do?
but I'd need to borrow your PC.
Numerical Approximations of pi (Wiki): Modern Algorithms
"These approximations have so many digits that they are no longer of any practical use, except for testing new supercomputers."

or I'd alternatively use the Gauss-Legendre Algorithm, but it might just be easier to run Super-Pi ;D

The necessary taylor series expansions of the arctangent function shouldn't be too hard to devise, I already did it a while back for the sin function: http://spreadsheets.google.com/pub?key=pTEZyJrzS1aK2U0P2QioQaw

Based on what I could find I would agree with Jason on 1,241,100,000,000 digits. Here is what I found:

"The largest number of decimal digits of pi ever computed is 1,241,100,000,000, that is, 1.2411 trillion. This staggering achievement was made in 2002 by computer scientist Yasumasa Kanada and his coworkers at the University of Tokyo Information Technology Center. Kanada's team programmed a Hitachi SR8000 supercomputer with a special formula for pi and ran the computer for over 600 hours. For more information about Kanada's computation, see the Science News Online article.

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80143857/25510582

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Anyone got any bigger answers than 80143857/25510582 for the most accurate computation of Pi here?

Otherwise Philadelphia wins.....

Luke.

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- Luke.

LOL, I found a bigger one 2646693125139304345/842468587426513207

Luke, I sent you a PM.

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Ok, currently Guido Man is winning... I'll run the competition out for another 4 hours, then I will approve a winner.

Remember!:
Question 71 (1 Point) : Create the best Pi approximation, e.g. 22/7, and show how many digits it is accurate to, you may refine your answer.

Luke.

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- Luke.

Guido.man, can I ask you where you got that figure from?

Q71:

Biggest I could find is

27225206761227411560482016369101495245580376291277469609660747193789333391455909056988538515440420244451/
8666052465496465627292667594900276640054365438839293273326351202074305984738201886052979281840113827831

gives

pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821

Luke.

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- Luke.