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Science problems thread: 2/7/2013 23:55:43


szeweningen 
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Hello,

Forum is a bit boring recently, so i'll try to start another thread similar to chess puzzles. Here the rules will be the same, one person posts a problem from one of the following fields:
- mathematics
- physics
- chemistry.


Problems should not exceed high school level, meaning no problems can be harder than the problems on International Olympiad from a given subject. If you want to post a problem on an academic level please state clearly it is significantly harder, otherwise it may stall the thread. Proofs can be given in links to pdf or similar formats if you need to use LaTeX.
The person who answers must post a new problem after the proof is confirmed!


Problem 1 - Number theory (Mathematics)

Prove that in the set of natural numbers there exist arbitrarily long sequences of consecutive numbers that are not prime numbers.


We're starting with an easy one, good luck! :)
Science problems thread: 2/8/2013 00:22:31


x 
Level 58
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This is a trick question, there is no such thing as a prime number.

Problem 2 - Juggalovian physics

Fucking magnets: how do they work?
Science problems thread: 2/8/2013 00:38:13

Seahawks 
Level 51
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there is a force between the positive energy and negative energy that pulls them together, the same force pushes the positives apart. This force is called electromagnetic force
Science problems thread: 2/8/2013 00:43:12

Seahawks 
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problem 3
there are ten numbered seats at a circular table numbered one - ten. five couples are going to be seated at a dinner party with the following restrictions.
(1): they must sit males and females alternating
(2): a person can not sit next to or directly across from his or her spouse.
how many combinations are there for the people to sit in?
Science problems thread: 2/8/2013 00:48:05


x 
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there is a force between the positive energy and negative energy that pulls them together, the same force pushes the positives apart. This force is called electromagnetic force


Um, the question was supposed to make you reflect upon the ineffable beauty of nature, but ok.
Science problems thread: 2/8/2013 00:59:35


szeweningen 
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Maybe no one noticed, but x's responce was not serious...

We are still on problem 1
Science problems thread: 2/8/2013 01:18:23

Seahawks 
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for problem 1 if all numbers in a set are multiplied together (1,2,3... y) then the sequence starting after multiplying 1 x 2 x 3... x y wont have any prime numbers until at least y +1 is added to the product decided because each number will be divisible by one of the numbers in the set because taking a multiple of a number x, and adding that number x to it, will always be divisible by x.
using this you can create longer and longer distances between prime numbers. Also, you only need to multiply together prime numbers because all non prime numbers are automatically divisible by a smaller, prime number because of the definition
Science problems thread: 2/8/2013 02:15:32


szeweningen 
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That is correct.

Solution to put it easier:

A sequence n!+2, n!+3,..., n!+n has n-1 consecutive composite numbers for any n>1.
Science problems thread: 2/8/2013 02:28:57

Seahawks 
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ok my question is the one i have put already
Science problems thread: 2/8/2013 03:06:49


professor dead piggy 
Level 59
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there isnt enough information to answer the question.
Science problems thread: 2/8/2013 03:27:58


professor dead piggy 
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You haven't told us how many couples are same sex. Obviously for every F-F pair there has to be a M-M pairing, so question works for 0,4 or 8 people paired with a member of the same sex. For 0 the answer is 2 possible combinations? I have no real proof because I have no idea how to write a proper mathematical proof. Each man can only be paired with 1 or 2 women on the table according to the rules. If he is paired with the left one then every other man has to be paired with the left. I wont bother solving for more same sex couples because im fairly sure you dont care and its hard. my question is solve seahawks problem with 2 same sex couples in the mix. I dont know the answer, i am sure its not hard, but it is boring. If you want to just lie and hit us with another question I wont call you out on it.
Science problems thread: 2/8/2013 03:28:38


professor dead piggy 
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1 *of 2 women
Science problems thread: 2/8/2013 03:30:16


nich 
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Is it 480?

Start by putting the men in odd seats, (1,3,5,7,9)

there are 5! possibilities here (five possible men to be chosen for seat 1 then four for seat 2 etc.)
Then for each combination there are only two women who can sit in seat 2 without breaking the rules (the wives of the men in seats 5 and 9). Also there are only two seats each woman may sit in (three places either side of their husband). This means there are only two seating arrangements of women for each of the 5! arrangements of men.

5! * 2 = 240
Double this for the case where women are in odd seats to get 480.
Science problems thread: 2/8/2013 03:32:03


nich 
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^ Assuming all 5 are heterosexual couples
Science problems thread: 2/8/2013 03:39:38


professor dead piggy 
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This isnt exactly a proof, but sze did ask that we link LaTeX if we used it: http://gifsoup.com/webroot/animatedgifs/980465_o.gif
Science problems thread: 2/8/2013 05:00:31

Seahawks 
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couples are all 1 male 1 female, sorry if there was confusion dead piggy, and nich was correct so its his turn
Science problems thread: 2/8/2013 07:54:42


Z-Dog 
Level 54
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I like this thread :)
Science problems thread: 2/8/2013 15:42:45


TheThedde 
Level 59
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Problem number 4, secondary alcohols (Chemistry)

What will you get if you oxidize a secondary alcohol?

(Lead: secondary alcohols are alcohols which the OH-group bind to a carbon atom, who bonds with two alkyle-groups (sorry for spelling)
Science problems thread: 2/8/2013 15:58:10


professor dead piggy 
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Science problems thread: 2/8/2013 16:54:35


TheThedde 
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Yes, a ketone
Science problems thread: 2/8/2013 17:58:57


professor dead piggy 
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question 5: prove 3.333recurring=1/3
Science problems thread: 2/8/2013 18:01:07


professor dead piggy 
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*ahem* question 5: prove 3.3recurring=10/3 and I will need to see you LaTeX for an answer to be considered valid.
Science problems thread: 2/8/2013 18:56:56


Moros 
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Well, since 3 fits three times in 10, with a 1 left.
And 0,3 fits three times in 1 as well, with 0,1 left.
And because the laws of maths say that if you divide something the comma (or whatever sign people use to separate decimals and whole numbers) moves one spot to the right, this continues forever. Thus 10/3=3,3333...
Good?
Science problems thread: 2/8/2013 18:59:10


professor dead piggy 
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Nope. Prove the "laws of maths". And do it quick before someone just googles the answer. This is actually an interesting fundamentally important tenet of mathematics, and noone ever knows it. It also creates arguments =D
Science problems thread: 2/8/2013 18:59:37


Moros 
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Sorry, I forgot this: http://www.latex-project.org/
Science problems thread: 2/8/2013 19:04:51


professor dead piggy 
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http://www.latex-project.org/

Noone wants to see that, you sicko. If you arent going to play the game then I wont give you any more hints.
Science problems thread: 2/8/2013 19:08:06


Moros 
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Haha, found it:
Science problems thread: 2/8/2013 19:09:35


Moros 
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Actually, that link will only lead you to a site describing LaTeX ;) You're being the sick one here.
Science problems thread: 2/8/2013 19:22:13


professor dead piggy 
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Haha, you think i didn't click a link called latex project? Great work, you are correct.
Science problems thread: 2/8/2013 19:36:12


Moros 
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Okay, here's a new problem:
What's the number of possible ways you can put notes and rests in a single 4/4 measure of sheet music? Not counting different clefs, and no notes or rests shorter than hemidemisemiquavers. And you can't just put lots of rests in different orders, but right next to each other, because when combined they last the same time. (I mean you can't have two quarter rests next to each other for example, because they would sound the same as a halve rest)

Good luck with that!
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