Super Duper Extra Hard Brainteaser

[gaming_mouse]

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I'm sorry I had other things to do and failed to continue reporting back every minute on the minute.

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forgiven.


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Since neither of us has a solution that we're happy with and I'm the one who appears to have the problem finding a suitable arbiter, I propose calling off the money portion of the bet but I'll change my location to your little pwned message for a month. This way we can all be unhappy about at least two things each and we can all move on.

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well, if you can live with yourself, I guess it's fine. I will offer you another suggestion if you are feeling more honorable. Write an email to a math professor at a school of your choice with this exact problem on it. I'll leave you on the honor system. If he writes back saying 1/2, pay us what you choose.

gm

[gaming_mouse]

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Edit - and mouse, let's just agree to disagree or something, I think we are getting caught up in the terms of the problem, and it's dumb anyway. But more importantly I have trouble sleeping with something like this still on going. So, if possible, don't even bother responding to my last post.

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that's fine. for the record, though, I'm really not trying to be defensive. I am quick and very willing to admit when I'm wrong, and I'm sure you can find many posts that prove that.

[hoyaboy1]

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Edit - and mouse, let's just agree to disagree or something, I think we are getting caught up in the terms of the problem, and it's dumb anyway. But more importantly I have trouble sleeping with something like this still on going. So, if possible, don't even bother responding to my last post.

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that's fine. for the record, though, I'm really not trying to be defensive. I am quick and very willing to admit when I'm wrong, and I'm sure you can find many posts that prove that.

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Yea, I realize you are a standup guy, which is why I am perfectly content to just end this.

[Patrick del Poker Grande]

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well, if you can live with yourself, I guess it's fine. I will offer you another suggestion if you are feeling more honorable. Write an email to a math professor at a school of your choice with this exact problem on it. I'll leave you on the honor system. If he writes back saying 1/2, pay us what you choose.

gm

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For the record, I do feel quite shitty about how this is ending. I'm not convinced I'm wrong, though, so I feel this is a fair solution. I'll give the e-mail a shot when I get a chance. I'm sure you'll get an opportunity to pwn me again some time when we can actually come to some concrete solution and then it will get paid off.

[BOTW]

Assume there are 400 two child families, we can have BB, BG, BS(arah), GB SB, SG or GS:

100 BB
99 BG
1 BS
99 GB
1 SB
98 GG
1 SG
1 GS

She says that she has a child named Sarah, so we are choosing among: 1 BS, 1 SB, 1 SG, and 1 GS. So it is 50% right?

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If the first girl isn't named Sarah, then the next one will be named Sarah 1/100 times. Probability of this is 99/100 * 1/100.

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The next one will be named Sarah more often to compensate for the fact that the first was not, no? Isn't it 1/99 times? Doesn't the math show it is 50% instead of 199/399, then?

This is interesting: www.wiskit.com/marilyn/boys.html

You meet a woman, and ask how many children she has, and she replies "two." You ask if she has any girls, and she replies "yes." After this brief conversation, you know that the woman has exactly two children, at least one of whom is a girl. When the question is interpreted this way, the probability that both of her children are girls is 1/3.

You meet a woman and her daughter. You ask the woman how many children she has, and she replies "two." So now you know that this woman has exactly two children, at least one of whom is a girl. When the question is interpreted this way, the probability that both of her children are girls is 1/2.

[DMBFan23]

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I'm sorry I had other things to do and failed to continue reporting back every minute on the minute.

[/ QUOTE ]

forgiven.


[ QUOTE ]
Since neither of us has a solution that we're happy with and I'm the one who appears to have the problem finding a suitable arbiter, I propose calling off the money portion of the bet but I'll change my location to your little pwned message for a month. This way we can all be unhappy about at least two things each and we can all move on.

[/ QUOTE ]

well, if you can live with yourself, I guess it's fine. I will offer you another suggestion if you are feeling more honorable. Write an email to a math professor at a school of your choice with this exact problem on it. I'll leave you on the honor system. If he writes back saying 1/2, pay us what you choose.

gm

[/ QUOTE ]

MY DRUNK EPIPHANY:

party girl is right. you were more right than me. we were both wrong.

it must be less than 1/2. it cannot be 1/2. partygirluk is right.

[jimdmcevoy]

Okay so there may be a slight problem in the original question, it seems gaming mouse is not happy with it, although I don't agree with gaming mouse that there is neccesarily a problem with it.

But I'll make this addition:

there are exactly 100 different names for girls, and a random girl is equally likely to be any of these names (1% each just like Sarah)

are you happy with this gaming mouse?

So now I am going to abandon my original answer of 199/399 and jump into the 1/2 camp. my new answer:

with only knowing the woman has two children the combinations and corresponding probabilities are:

boy boy - 1/4
boy sarah - 2/400
boy non-sarah - 198/400
non-sarah non-sarah - 98/400
sarah non-sarah - 2/400

so now when you find out she has a girl named sarah it is clear it's a 50/50 the other child is a boy/non-sarah

my mistake before was figuring the odds of the last two terms, I didn't take into account the fact that if you didn't name the first girl sarah, there will now be a 1/99 chance you name the second girl sarah, not 1/100

[DMBFan23]

partygirl is right. anything else is posturing.

[DMBFan23]

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He's totally backing down. I'm a nice guy, though. I would let Patrick off the hook for $50 and Patrick changing his location for the next month to "Getting pwned by GM & jason_t".

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you guys were owned by party girl, and so was I. I have admitted I was wrong, and so should you both. and change your locations to reflect your arrogance.

[jimdmcevoy]

It's funny, at the same time you switched to agree with partygirl, I switched away from party girl

One thing I have going for me is i'm on gaming mouse's team now