benjer3

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curr3nt made it preatty clear who he was... unfortunatelly he redirected lex to himself last night .. (saving aura or nana I think .. or maybe mike  but I think he saved aura) so it's not like Panther described it....
Wait, are you admitting that you're a baddie? How else would you know these things?

BrainIAC: Ysan
Roster:
1) Hirkala  DEAD [?] Killed by Hawkgirl
2) marquessa  DEAD [?] Killed by Villains
3) curr3nt  DEAD [?] Killed by Villains
4) Molly Mae
5) Yodell
6) TheChad  DEAD [Sinestro] Lynched
7) Panther  voting for Molly Mae
8) Framm
9) MikeD  voting for Molly Mae
10) nana77 voting for Molly Mae
11) TwoaDay  voting for Molly Mae
12) jay
13) Flamebirde DEAD [?] Killed by Villains
14) Aura
15) benjer3  voting for Molly Mae
I guess we're going after Molly.

BrainIAC: Ysan
Roster:
1) Hirkala  DEAD [?] Killed by Hawkgirl
2) marquessa  DEAD [?] Killed by Villains
3) curr3nt  DEAD [?] Killed by Villains
4) Molly Mae
5) Yodell
6) TheChad  DEAD [Sinestro] Lynched
7) Panther
8) Framm
9) MikeD
10) nana77
11) TwoaDay
12) jay
13) Flamebirde DEAD [?] Killed by Villains
14) Aura
15) benjer3  voting for Panther
I suppose I'll start the voting....

It would count as block on block, and as the per OP, that results as a canceling out of the blocking action.
Though Nana isn't quite cleared yet. She could still be Sinestro. But that doesn't mean I don't trust her. Though that doesn't mean I completely do, either.

BrainIAC: Ysan
Roster:
1) Hirkala  DEAD [?] Killed by Hawkgirl
2) marquessa  DEAD [?] Killed by Villains
3) curr3nt
4) Molly Mae
5) Yodell
6) TheChad  voting for Framm
7) Panther  voting for Jay
8) Framm  voting for Molly Mae
9) MikeD  voting for TwoaDay
10) nana77  voting for TheChad
11) TwoaDay
12) jay
13) Flamebirde DEAD [?] Killed by Villains
14) Aura
15) benjer3  voting for TheChad
Putting needed pressure on, and I trust Nana for now.

BrainIAC: Ysan
Roster:
1) Hirkala
2) marquessa
3) curr3nt
4) Molly Mae
5) Yodell
6) TheChad
7) Panther  voting for Benjer
8) Framm  Voting for jay
9) MikeD
10) nana77  voting for Benjer
11) TwoaDay
12) jay
13) Flamebirde DEAD [?] Killed by Villains
14) Aura  voting for Benjer
15) benjer3  voting for Hirkala
Wow, wasn't expecting that. Well I'm not going to lie, I did target you last night. But you being blocked prevented my action from going through....
As for my vote, it's just random.

Adsum!

If the player loses his stake after a loss, then he will end up with $0 no matter what.
To illustrate:
Round 1: Total = $1, Stake = $1, Loss = $0, Win = $2
Round 2: Total = $2, Stake = $2, Loss = $0, Win = $4
Round 3: Total = $4, Stake = $4, Loss = $0, Win = $8
.
.
.
To summarize, by doubling his stake each round, he keeps betting all his money. Since he will eventually lose, he will eventually lose all the money he won plus the dollar he started with.

At first, I thought it would be impossible to determine anything from just one draw, but then I realized that there is a chance that you draw the added ball, which can give us a probability for the added ball.
I first imagined that there are 2 blue balls, 1 red ball, and 1 unknown, and that we drew a blue ball. The chances that the added ball is red depend on the ball drawn as follows:
blue1: 50%
blue2: 50%
red1: 50%
unknown: 0%
Each possible scenario can then be averaged together to give a probability of 1/3rd that the added ball was red.
From there, it was easy to realize that the drawn blue ball will always be either one of two first blue balls, or the added ball. That would make it so the probability that the added ball was red is 1/3rd no matter how many red balls we started out with.
I do have my doubts about my solution, but it's the best I got. And after all, I thought it was impossible at first.

BrainIAC: Ysan
Roster:
1) Hirkala
2) marquessa
3) curr3nt
4) Molly Mae
5) Yodell
6)
7) Panther
8) Framm
9) MikeD
10) nana77
11) LJ
12)
13) Flamebirde
14)
15) benjer3
Backups:
1) Brainiac100
2)
Oh alright, I'll join. Though it may mean playing 4 games, hosting a nonmafia, and taking care of the MM wiki all at once.

class Program { static void Main(string[] args) { Random random = new Random(); int numberOfFamilies = 1000; int numberGirlGirl = 0; int numberBoyGirl = 0; int numberBoyBoy = 0; int numberGirlBoy = 0; for (int count = 0; count < numberOfFamilies; ++count) { Family family = new Family(); int childIndex = random.Next(2); bool firstChild = family.Children[childIndex]; bool otherChild = family.Children[(childIndex == 0) ? 1 : 0]; if (firstChild) { if (otherChild) { ++numberGirlGirl; } else { ++numberGirlBoy; } } else { if (otherChild) { ++numberBoyGirl; } else { ++numberBoyBoy; } } } Console.WriteLine("Out of {0} families, there were {1} girlgirls ({2}%), {3} girlboys ({4}%), {5} boygirls ({6}%), {7} boyboys ({8}%).", numberOfFamilies, numberGirlGirl, (double)numberGirlGirl / (double)numberOfFamilies * 100D, numberGirlBoy, (double)numberGirlBoy / (double)numberOfFamilies * 100D, numberBoyGirl, (double)numberBoyGirl / (double)numberOfFamilies * 100D, numberBoyBoy, (double)numberBoyBoy / (double)numberOfFamilies * 100D); Console.ReadLine(); } } public class Family { private static readonly Random random = new Random(); public bool[] Children = new bool[2]; public Family() { for (int index = 0; index < Children.Length; ++index) { Children[index] = random.Next(2) == 1; } } }
This yields "Out of 1000 families, there were 239 girlgirls (23.9%), 247 girlboys (24.7%), 280 boygirls (28%), and 234 boyboys (23.4%)." Nearperfect distribution.

so what were the other 485? If you're claiming that they're boys, then that makes 485*2 boys = 970 + (244 out of your 515 families) which leaves 786 children of whom 271 are girls.and the other 515 are ???.
Or are you taking it that the girl you've been introduced to is the eldest child?
In the other 485, all of the "other children" were boys, and the first children could be boys or girls. I could modify the program to show that the first children were equally distributed among boys and girls in this group as well. That leaves 515 "other" girls, 485 "other" boys, (271 + ~0.5 * 485) "first" girls, and (244 + ~0.5 * 485) "first" boys, giving a near perfect distribution. And if you look at the program, I randomly select from the first and second child of the family (though it wouldn't make a difference either way; I just did that to make it more realistic), so I'm not assuming anything about the children I've been introduced to.

On the contrary. Look at this program (and let me know if it's wrong ):
class Program { static void Main(string[] args) { Random random = new Random(); int numberOfFamilies = 1000; int numberSecondGirl = 0; int numberGirlGirl = 0; int numberBoyGirl = 0; for (int count = 0; count < numberOfFamilies; ++count) { Family family = new Family(); int childIndex = random.Next(2); bool firstChild = family.Children[childIndex]; bool otherChild = family.Children[(childIndex == 0) ? 1 : 0]; if (otherChild) { ++numberSecondGirl; if (firstChild) { ++numberGirlGirl; } else { ++numberBoyGirl; } } } Console.WriteLine("Out of {0} families, {1} of the \"other children\" were girls. Out of those, {2} of the first children were girls ({3}%), while {4} of them were boys ({5}%)", numberOfFamilies, numberSecondGirl, numberGirlGirl, ((double)numberGirlGirl / (double)numberSecondGirl) * 100D, numberBoyGirl, ((double)numberBoyGirl / (double)numberSecondGirl) * 100D); Console.ReadLine(); } } public class Family { private static readonly Random random = new Random(); public bool[] Children = new bool[2]; public Family() { for (int index = 0; index < Children.Length; ++index) { Children[index] = random.Next(2) == 1; } } }
For one run, this resulted in "Out of 1000 families, 515 of the 'other children' were girls. Out of those, 271 of the first children were girls (52.6%), while 244 of them were boys (47.4%)." The results are kinda backwards from what you stated, but I think you get the idea.

Hmm, I think I've had a breakthrough. Let me put it in terms of the OP:
A parent comes up to you and says, "I have two children and one of them is a girl." They then proceed to tell you the gender of the other child. Being the analytic people that we are, we wonder what the odds that the second child was a girl were. While we ponder this, another parent happens to come up and says, "I have two children and one of them is a boy." A hundred parents then proceed to do the same, with the gender of the first child varying. (It also just so happens that, if each parent has at least one girl, they will say, "One of them is a girl.")
Now I ask, can we just discard the cases where the first child was a boy? I propose not, for in doing so we would be selectively taking members out of a sample group that needs to be complete, not to mention skewing the results by doing so selectively. So what are we to do? What if we changed our question, while keeping the same general idea intact: "Given the gender of one in two children, what are the odds that the other is a girl?" This question encapsulates the original question, as well as allowing for other scenarios. But now the answer is obvious, isn't it. In this question, it is obvious that the gender of the "other child" is completely independent of the gender of the first. And thus its answer can be nothing other than 50%.
So think what you will. I did change the question, but as I said, I believe the question is a perfect substitute for the original as it asks the exact same thing but allows for a complete sample group.

Oh good grief.
Sorry, I'm always doubting myself.

Hmm, you do have a point. And I'm beginning to think that this question cannot be answered by experimentation. The reason I say that is surveying about the genders of people's children is very different from them just coming out and telling you. If you ask people about their children, you have no prior knowledge and thus have to remove those cases where you do not get the results you want. However, if a bunch of people come up and tell you the same condition (that they have two children and one girl), every case has to be considered; no case is just thrown out, meaning there's no dropping of combinations. So now the question I'm pondering is, if a thousand people come up to you and say said condition, how many of the unmentioned children are girls?
In this case, there are only two possible scenarios. Either the unmentioned is a girl or a boy. You can't consider the four cases, because that assumes that we took our sample families out of a larger group of families with any possible combinations, but that is not the case. We have our sample population; we can't compare it to the rest of the population. So I would have to say my answer to the original question is 50%.

Did you get to the end of my post? I came to a very important conclusion, I think. Your program assumes that the parents randomly told us the gender of one of their children, which is perfectly logical. On the other had, mine assumes that if a girl is present, the parents would mention that, as that is what we're testing for. I believe that that is the whole teaser in a nutshell. It all depends on how you test it. The problem is, the 1/3ists can't prove the 1/2ists wrong as any 1/3ist proof doesn't apply to the 1/2ists, and vice versa.
Let's do a little mind experiment. Say we went to test this out for real. You go around asking parents with two children what the gender of one of their children are, while go around asking if one of their children are a girl. You then (if they say a girl) ask the gender of the other child, while I (if they respond yes) do the same. Our results will be obvious: about 1/2 of your second children will be girls, while about 1/3 of mine will be girls. Did we do something wrong? Well yes and no. Yes because we tested for two completely different things. I can't say to you, nor you to me, "You should have gotten my results," because we each tested for something different. However, there is nothing wrong with either of our methods of testing.
The big question now is which is right? I propose that they are both right. It just depends on how you read the question. So if anyone ever points a gun at your head and asks you, "I have two children. One of them is a girl. What's the gender of the other one?" you should first ask him, "If you had a boy and a girl, would you tell me one was a girl, or would you pick arbitrarily between them?"... and that would probably leave him stumped enough for you to get away.
 1

Wow, I was a doubter, but I have to say I'm impressed. The question I will ask all of you, before all of your bickering and mathematics, is have you tried it out? I wrote a simple program to chuck out the numbers, and the results are pretty astounding. (If someone has already done this, forgive me, but I didn't feel like going through 32 pages checking for it.) I also have to say that in writing the program, I see why it gets the results it gets.
Here's the code (in C#):
static void Main(string[] args) { int secondGirls = 0, secondBoys = 0; for (int count = 0; count < 1000; ++count) { Family family = new Family(); if (family.Child1  family.Child2) { Console.Write("Family1 has a girl. "); if (family.Child1 && family.Child2) { Console.Write("The other child is a girl.\n"); ++secondGirls; } else { Console.Write("The other child is a boy.\n"); ++secondBoys; } } } Console.WriteLine("Of the second children, {0} are girls and {1} are boys", secondGirls, secondBoys); Console.ReadLine(); } } public class Family { private static readonly Random random = new Random(); public bool Child1 = random.Next(2) == 1; public bool Child2 = random.Next(2) == 1; }
"Of the second children, 249 are girls and 492 are boys."
This means that for every family where one child was a girl, there was 1/3 of a chance that the other child was a girl.
Think of it as you will, but this program is short, sweet, and to the point, and I think fullproof.
I can also see where some people will argue with my methods. The main point they will make is that I intentionally dropped out the 1/4 of the families with both boys, thus conforming to what the 1/3ists say. However, I repeat that I was a doubter at first. I thought that this experiment would show that the probability is 1/2.
The main point of the puzzle is that there are already two children, not one child with another being born. I set up my program to set up each family before testing it. If both were boys, I simply discarded the family as it didn't apply to the puzzle. If I had set it up so that the second child was determined only after the first was determined to be a girl (as in a birth scenario), I would obviously get a 5050 result.
That being said, I see both sides very clearly now, and I imagine the bickering will continue, as my code clearly "leans toward" the 1/3ist's perspective. All I'll say is the results of this experiment turned my thoughts around. Maybe, just maybe, both sides are right, and it really all depends on how you look at the problem.

Also, Wolfgang, that is interesting. Like maybe Israel is chosen because they are the direct descendants of Adam and Eve.

How on earth does the story of Cain support your idea that evolution is guided by a supernatural force?
Please don't be angry at me. Despite what you probably think, that theory is not at all founded in my religious beliefs. Like I said, I'm very logical. And I often doubt things in my religion due to that. I'm just lucky my religion is very logical as well.
And also, when anger is involved, I tend to go with the side that's less angry, because that usually means they have their stuff together....

The detrimental mutations die out while the beneficial ones thrive.
But wouldn't those with the rare beneficial mutations be already riddled with detrimental mutations?

How can a species survive all of its detrimental mutations just with a few beneficial mutations every now and then?
Or not survive per se. I mean how can it grow in complexity when most of it's mutations are detrimental?

It's not from "pure evolution." It's from evolution through natural selection. And natural selection does account for increased complexity.
I'm talking about natural selection, too. When I say "beneficial mutation" I mean one that gives them a greater chance of survival. But say a species just underwent a beneficial mutation, and then those with the mutation outsurvive those without it. (And I know evolution is not this linear, but I believe talking about it this way is sufficient.) It will probably be hundreds of years before the next beneficial mutation in the population, and during that time there will be countless detrimental mutations. How can a species survive all of its detrimental mutations just with a few beneficial mutations every now and then? (And forgive me for not being very knowledgeable about all the facts and figures. The furthest I have gone in biology so far is my high school advanced biology course. There may be facts that completely destroy my theory, but I haven't heard any yet.)

From what I've heard, in the original Hebrew of the Old Testament, the actual wording is a period of time, but that was translated to a "day."
As to the rest of it. I am personally wary of evolution, and that's not because I'm religious but because I'm logical. I can see the earliest beginnings where the primordial soup formed the basics of life, and I can see the very end where evolution and natural selection are making subtle changes in species. However, I can't for the life of me see the middle.
If you think about it, once you get even only to the first singlecelled creatures, hardly any mutations will be beneficial. The chances are probably in the range of one out of a billion or so. That would mean you need billions of one species for a few to have beneficial mutations. Then the mutants have to be able to survive long enough to make a billion more of their kind, with many more, probably detrimental mutations getting in the way. While getting to the proper numbers probably wouldn't be a problem in the bacterial world, there is still a lot going against even them probabilitywise.
If you look deeper into the probabilities, you will realize that for every beneficial mutation, there will be millions of other mutations, most of them detrimental. The only way greater organization can come out of that is with incredibly large numbers. Again, this isn't much of a problem for bacteria, but when you carry this over to the multicellular world, I see major problems.
Today we're worried about the genomes of species, including ourselves, degrading rather than continuing to evolve, for the same reasons that I just mentioned. So how could species have evolved so far up to this point, but only just now have genomic problems? I know some of it has to do with the lack of natural selection, especially in humans and agricultural breeds, but in no way does that cover all of it. The only solution I can come up with is divine intervention. Without it, I can't see any hope for complex life.
So to get back to your theory, I believe all the species we're created by God through evolution. I don't think significant complexitybuilding evolution is possible without God. Some species may have evolved on their own, but from my observations, none of them are more complex than their ancestors. So maybe there was one race of mankind that other species diverged from, or maybe primitive manlike beings did evolve from apes, but I can't see equals to humans being the offspring of pure evolution.
 1
Red hat, blue hat
in New Logic/Math Puzzles
Posted