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Maths vs Me

29 Aug 09 | Re: Unavoidable parity

There’s another mistake in the last posting, about the one-child policy: I only accounted for 1023 of the couples. There should have been one couple with nine children, and one that has ten or more. Without actually working it out, I’m willing to pretty much guarantee that the final couple has an average expectation of 11 children, bringing the real total expectation to exactly 1024 boys and 1024 girls - complete parity.

So to summarise:

• If everyone has one child, you get equal boys and girls.
• If everyone keeps going until they get a boy no matter how many girls they have, you get equal boys and girls.
• If everyone who has a boy first has to stop, but those who have a girl can have one extra child in the hope of getting a boy, you STILL get equal boys and girls (work it out if you don’t believe me).

It looks like no matter how much maths you do, you can’t get away from equal boys and girls. Bah! Or is there some mathematician out there with a clever rule that would get round this?

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