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Philadelphia Send message Joined: 12 Feb 07 Posts: 1590 Credit: 399,688 RAC: 0 |
That was quick Philly! And yes the answer is right ;) Congratulations! 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%. |
Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
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. - Luke. |
Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
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Fred W Send message Joined: 13 Jun 99 Posts: 2524 Credit: 11,954,210 RAC: 0 |
Any Answers? Q69: It is prime. (And if I am wrong, the next poster gets the point?) F. |
W-K 666 Send message Joined: 18 May 99 Posts: 19087 Credit: 40,757,560 RAC: 67 |
Any Answers? As 2,438,100,000,001 is 300^5 + 300^4 + 1, I would say it has to be composite. |
William Rothamel Send message Joined: 25 Oct 06 Posts: 3756 Credit: 1,999,735 RAC: 4 |
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. |
Fred W Send message Joined: 13 Jun 99 Posts: 2524 Credit: 11,954,210 RAC: 0 |
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 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. |
Dominique Send message Joined: 3 Mar 05 Posts: 1628 Credit: 74,745 RAC: 0 |
Any Answers? 2438100000001 = 73*33398630137 Not prime |
Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
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. - Luke. |
Philadelphia Send message Joined: 12 Feb 07 Posts: 1590 Credit: 399,688 RAC: 0 |
Ok, another big response..... 7 |
William Rothamel Send message Joined: 25 Oct 06 Posts: 3756 Credit: 1,999,735 RAC: 4 |
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 |
Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
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. - Luke. |
Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
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jason_gee Send message Joined: 24 Nov 06 Posts: 7489 Credit: 91,093,184 RAC: 0 |
No Answers? 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 "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. |
Philadelphia Send message Joined: 12 Feb 07 Posts: 1590 Credit: 399,688 RAC: 0 |
No Answers? 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. |
Philadelphia Send message Joined: 12 Feb 07 Posts: 1590 Credit: 399,688 RAC: 0 |
80143857/25510582 |
Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
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Philadelphia Send message Joined: 12 Feb 07 Posts: 1590 Credit: 399,688 RAC: 0 |
LOL, I found a bigger one 2646693125139304345/842468587426513207 Luke, I sent you a PM. |
Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
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Luke Send message Joined: 31 Dec 06 Posts: 2546 Credit: 817,560 RAC: 0 |
Guido.man, can I ask you where you got that figure from?
Luke. - Luke. |
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