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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted May 16, 2010 01:53 AM |
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Edited by dimis at 01:54, 16 May 2010.
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Q16. Bacteria in a Glass
Q16. A number of bacteria are placed in a glass. One second later each bacterium divides in two (of equal size as the initial), the next second each of the resulting bacteria divides in two again, etc. After one minute the glass is full. When was the glass half-full ?
Regarding the fairness of Risk, I don't know what to say Corribus. Clearly the whole randomization comes from the dice, so, the first idea is to manipulate the dice and make them uneven so that the end result is fair. If you have a look at the end of the paper I gave earlier with a link (Section Conclusion and Recommendations), you will see that in RISK II people nowadays are throwing non-uniformly distributed dice and they have simultaneous turns.
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The empty set
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ihor
Supreme Hero
Accidental Hero
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posted May 18, 2010 07:14 PM |
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Edited by ihor at 19:15, 18 May 2010.
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I guess we should go on.
That puzzle is with catch in it. Don't know why nobody posted yet.
Answer: after 59 seconds.
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Corribus
Hero of Order
The Abyss Staring Back at You
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posted May 18, 2010 07:18 PM |
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It was never half full. At best it was half empty. 
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ohforfsake
Promising
Legendary Hero
Initiate
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posted May 18, 2010 07:26 PM |
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What a pesimistic view! 
[Actually, seriously, I often meet people who says half full is positive and half empty is negative, for me it's the other way around. It's so, because when something is half full, it focuses on not being completely full, i.e. it could be better [not satisfied with current conditions]. When something is half empty, it focuses on it's not completely empty, i.e. it could be worse [satisfied with current conditions].
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Living time backwards
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ihor
Supreme Hero
Accidental Hero
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posted May 18, 2010 07:43 PM |
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This is rubbish.
I often say half full and often half empty. Does that mean I'm pessimist and optimist all in one, or that indicates my mood?
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted May 18, 2010 07:47 PM |
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It's just about in what direction it goes.
If you want someone to fill your glass, you hardly say "Please make it half empty!", no matter if you're a pessimist or not..
Similar to the names you give when telling the time. Until 30 minutes, you say "...past...", after that, you say "...to..."
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Better judged by 12 than carried by 6.
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Corribus
Hero of Order
The Abyss Staring Back at You
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posted May 18, 2010 07:58 PM |
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Q17.
What is the next number in the sequence:
1, 1, 2, 9, 144, 4255, ....
(note, number sequence problems often have more than one possible correct answer!)
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Binabik
Responsible
Legendary Hero
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posted May 23, 2010 01:42 AM |
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0, 1, 1, 2, 9, 144, 4255
btw, is there maybe a typo in your post?
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Corribus
Hero of Order
The Abyss Staring Back at You
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posted May 23, 2010 02:50 AM |
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Wow, geez did I screw that up!
Sorry, yes.
The proper sequence is: 1, 1, 2, 9, 96, 2500....
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I'm sick of following my dreams. I'm just going to ask them where they're goin', and hook up with them later. -Mitch Hedberg
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friendofgunnar
Honorable
Legendary Hero
able to speed up time
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posted May 23, 2010 06:45 PM |
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Here's the mathematical solution to the second risk problem I posted. I decided to tackle it by breaking it down into smaller components. Basically there's four parts. The first part works out how you do when you're rolling 3 dice versus 2. The second part is when you're rolling 3 dice versus 1. The third part is when you're rolling 2 dice versus 1. Then everything gets wrapped up in the end. Since this is the "conserving strength" scenario, any time you end up in a situation with losing odds (1 v 2, 2 v 2, 1 v 1) the battle is over.
So you can see your best bet is to go with the 5 and 4 instead of the 6 and 3. The trade-off I think is that if you don't take the territory you're more likely to have less armies to use for the next turn.
The opposite happens if you go the other way, 7 & 2 vs 3.
(statistical)
6 & 3 vs 3, conserve strength: 70.14 %
7 & 2 vs 3, conserve strength: 81.73 %
It's interesting though that the "win at all costs" scenario replicates the "conserve your strength" scenario although the differences aren't as large.
(statistical)
6 & 3 vs 3, win at all costs: 86.96 %
5 & 4 vs 3, win at all costs: 87.44 %
You can see a complete breakdown here:
btw thanks again for the math lesson Dimis 
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Mytical
Responsible
Undefeatable Hero
Chaos seeking Harmony
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posted May 25, 2010 08:29 AM |
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Edited by Mytical at 09:45, 25 May 2010.
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Ok, need some help figuring up a formula for current over all score in a class. Have the averages, and how many percent each is worth..don't need the answer really..a formula will do. Know I should know it, but mind has gone blank.
Average of current grades - Percent of overall grade its worth.
.905 (out of 1) - 40% of total grade.
.9125 (out of 1) - 30% of total grade
.895 (out of 1) - 15% of total grade
1 (out of 1) - 5% of total grade.
Still have a final worth 10% but won't know that for a bit. It SEEMS like it should be (.905 x .4) + (.9125 x .3) + (.895 x .15) + (1 x .05)..is that even CLOSE to correct?
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Message received.
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winterfate
Supreme Hero
Water-marked Champion!
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posted May 25, 2010 09:25 AM |
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Looks completely correct from where I'm sitting. At the end, multiply that result by 4 and it SHOULD tell you your final grade. 
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If you supposedly care about someone, then don't push them out of your life. Acting like you're not doing it doesn't exempt you from what I just said. - Winterfate
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Mytical
Responsible
Undefeatable Hero
Chaos seeking Harmony
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posted May 25, 2010 09:39 AM |
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Edited by Mytical at 09:41, 25 May 2010.
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Hmm if I multiply it by four, I seem to come out with 328%? That can't be correct. Don't you mean multiply it by 100 to change it from a percent to a whole number?
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Message received.
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winterfate
Supreme Hero
Water-marked Champion!
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posted May 25, 2010 09:41 AM |
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That huge number translates to 3.28/4.00.
I was thinking of how it'd look based on the four point system. 
Technically, you don't actually have to multiply at all. What you get with your formula is your current grade in percents.
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If you supposedly care about someone, then don't push them out of your life. Acting like you're not doing it doesn't exempt you from what I just said. - Winterfate
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Mytical
Responsible
Undefeatable Hero
Chaos seeking Harmony
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posted May 25, 2010 09:42 AM |
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Ah ok. I understand! Got it. Thank you.
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Message received.
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winterfate
Supreme Hero
Water-marked Champion!
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posted May 25, 2010 09:43 AM |
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No problem. 
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If you supposedly care about someone, then don't push them out of your life. Acting like you're not doing it doesn't exempt you from what I just said. - Winterfate
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friendofgunnar
Honorable
Legendary Hero
able to speed up time
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posted May 25, 2010 01:03 PM |
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So recently I've been reading some books on mathematics and mathematicians and it got me to thinking about this thread. If I remember correctly both Ecoris and Dimis were professional mathematicians of some type so I was wondering what exactly you guys do and what your field of specialty is. Also I'm curious about the other posters in this thread like Ihor and Ohfor and whether you guys use math professionally also?
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Corribus
Hero of Order
The Abyss Staring Back at You
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posted May 25, 2010 03:40 PM |
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As I think many people here know, I'm a chemist, so I use math quite frequently.
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I'm sick of following my dreams. I'm just going to ask them where they're goin', and hook up with them later. -Mitch Hedberg
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ohforfsake
Promising
Legendary Hero
Initiate
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posted May 25, 2010 07:05 PM |
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Don't know what you mean by the word profesional. To me it means that a person is paid for it.
In Denmark you get money for taking an education when you're above a certain age, so you could say I use it profesionally, though it seem to be stretching the defintion on an environment it wasn't intended in my opinion. (That you get paid no matter how good you are).
Btw. I study physics at Copenhagen uni.
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Living time backwards
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ihor
Supreme Hero
Accidental Hero
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posted May 25, 2010 10:32 PM |
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Now I'm just a student of the faculty of mechanics and mathematics in Lviv, Ukraine. This exam session and one more year to study in the uni.
I have studied Math more advanced from 14 yo when entered lycee specialized in physics and mathematics. And now I believe one part of my uni group (me together with my colleagues who also graduated from lycee - 5 from 50) is much stronger in Math than others, but we often help them.
As for speciality I deal with theory of functions of a complex variable (Complex Analysis) and especially Nevanlinna's theory of value distribution.
Finally I believe studying Math gives not only possibility to calculate quickly or solve simple tasks, it provides another way of thinking. It teaches not only trust everything but pushes to check it. In this way I use Math every day.
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