I find making these kinds of connections among seemingly disparate topics or concepts fascinating. I wonder what kind of model could be used do this in an automated way?

]]>[spoiler]

it ends up being a 1:1 ratio

50% boys | 50% girls (50% boys | 50 % girls(etc…))

The count will always be equal.

[/spoiler] ]]>

– I know you said that it could be solved using common sense, but I prefered to take an approach using algebra since you did not specify the population or number of couples.

1. His decree would not work because there would be slightly more boys than girls.

2. There would be an average of 2 children per couple. [/spoiler]

Here is how I did it:

[spoiler] I realised that since we are using an unknown population, though number of couples is more accurate for the method I believe I solved it. I figured that with a given population, say 4096 couples you could figure out the number of boys to girls that would be born. You said there was a 50-50 shot of whether there was a boy or girl. So if 4096 couples were to have children, then 2048 would have a boy and stop and the other 2048 would have a girl, and keep trying so I came up with a list (that unfortunally due to formatting I can not post) granted the total number of couples adds up to 4095 out of 4096, in the theory of X number of couples, I theorise all the numbers would add up: [/spoiler]

*A chart would be here if formating allowed* Spoiler Continued [spoiler]

Total Number of Children = 8178

Boys = 4095

Girls = 4083

Average Number of Children per Couple = 1.997–> 2 children per couple [/spoiler]

My Question: [spoiler] So I do have a question for you guys if you could help me out with it, I decide to use an exponetial of 2 since there was a 1/2 chance (since I was going opposite was 1/2->2/1=2)

So I figure I could figure out how many boys and girls given any population using this system of equations:

# of Couples n = 2^X

# of Boys b = n or b = 2^x

# of Girls g = b – x or g = (2^x) – x

X being exponetial growth from 2 to the # of couples

I was wondering if this system would work; if given any number of couples would it produce the correct number of boys and girls? And if so then the boys to girls ratio would be:

n : n – x [/spoiler]

Anyways that is how I figured it out, and that is what I believe my answer to be, and thank you for taking a look. Let me know,

Jonathan