Sultan's law involving outnumbering A Sultan wanted to increase the number of women in his country, as compared to the number of men, so that men could have larger harems. (Sorry ladies!) To accomplish this, he proposed the following law: As soon as a mother gave birth to her first son, she would be forbidden to have any more children. In this way, the Sultan argued, some families would have several girls, and only one boy, but no family would have more than one boy. It would not be long before the females greatly outnumbered the males. Do you think the Sultan’s law would work? This problem is considered a math problem which i think is pretty interesting. I've read this problem to a couple of people and here is what we thought: 1. What if every women gives birth to a boy, then this would not work. I'm not sure what factors are controlled in this problem but any ideas?

No, it would not! the shortest explanation is the sanity check, "why does when I stop having babies influence the babies I have already had?"

Though, perhaps easier to understand is, if you look at a single woman, the expected number of male children is 1, and the expected number of female children is 1/2 for the first + 1/4 for the second + 1/8 for the third + ... =1.