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Mathematics constants, variables and stuff

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Old 04-18-2012, 09:00 PM   #1782446  /  #1
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Programming / math

http://projecteuler.net/
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Old 04-18-2012, 09:03 PM   #1782451  /  #2
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I forwarded that to a math professor I know.
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Old 04-18-2012, 09:50 PM   #1782513  /  #3
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I know a nerd who likes puzzles!
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Old 04-18-2012, 09:56 PM   #1782523  /  #4
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hmm
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Old 04-18-2012, 10:06 PM   #1782531  /  #5
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This is trivial. You might be able to come up with some really cool algorithms that compute the sum in a particularly clever way, though.
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Old 04-18-2012, 10:16 PM   #1782538  /  #6
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that's what I was thinking. What is a non-standard approach to this?
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Old 04-18-2012, 11:05 PM   #1782568  /  #7
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Quote:
Originally Posted by TestyCalibrate View Post
that's what I was thinking. What is a non-standard approach to this?
Exponential sum.
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Old 04-18-2012, 11:06 PM   #1782569  /  #8
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wait, what? can you give an example?
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Old 04-19-2012, 12:17 AM   #1782604  /  #9
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Quote:
Originally Posted by TestyCalibrate View Post
wait, what? can you give an example?
OK, a mathematical solution:

Even-valued terms are every 3 terms (as the Fibonacci sequence mod 2 is 0, 1, 1, 0, 1, 1, 0, ...). There is a formula for the nth term of the Fibonacci sequence which goes as follows:



There are 33 fibonacci numbers (starting with F(1) = 1) less than 4 million. Therefore the sum is:







In order to prevent extra math, we figure out the denominators now.





Therefore by cross-multiplying we get






ETA: My nerditude has reached a maximum.
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Old 04-19-2012, 12:41 AM   #1782633  /  #10
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that just pisses me off.
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Old 04-19-2012, 12:43 AM   #1782635  /  #11
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I think I had some kind of integral approximation in mind, but I don't remember precisely.
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Old 04-19-2012, 03:00 AM   #1782743  /  #12
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There's a ton of equations relating to Fibonacci numbers.

Another way to calculate the solution:



For the sum of every third member of the series starting from n = 0:



From this recurrence and the first 3 terms of the sum we get the matrix equation:

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Old 04-23-2012, 09:51 PM   #1787251  /  #13
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I've completed 1-20. Only 361 to go.
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Old 04-24-2012, 08:22 AM   #1787787  /  #14
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I have solved them. Have you got anything harder?
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Old 04-25-2012, 02:41 AM   #1788893  /  #15
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Old 04-25-2012, 03:00 AM   #1788954  /  #16
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Got it.
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Old 04-25-2012, 06:10 AM   #1789130  /  #17
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Is it 2? that is at least consistent anyway.
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Old 04-26-2012, 03:14 PM   #1790393  /  #18
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Haha, that took me far too long.

eta: it's a good one, so obvious when I thought about.
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Old 04-26-2012, 03:19 PM   #1790402  /  #19
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Took me about 2 minutes but I think only because I hit on the right strategy first.
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Old 04-26-2012, 03:22 PM   #1790404  /  #20
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Yeah, I just couldn't think of what a kid might see, but like so many things in life, it came to me while I was having a piss.
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Old 04-26-2012, 04:45 PM   #1790547  /  #21
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2 days later I'm still trying to figure it out.

I must be a freaking genius!!
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Old 04-26-2012, 04:48 PM   #1790548  /  #22
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the clue that a kindergartener can figure it out pretty quick helps a lot.
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Old 04-26-2012, 04:50 PM   #1790552  /  #23
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I got it!!!
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Old 04-26-2012, 04:55 PM   #1790559  /  #24
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see? Think like a kindergartener.
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Old 04-26-2012, 04:56 PM   #1790560  /  #25
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Actually I was thinking: What Would Testy Do?

;coolio;
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