Monthly Brainteaser and June’s AnswerTuesday, July 5th, 2011
Last month we posted the following lengthy problem:
The ancient city state of Sparta has had, for as long as anyone could remember, the same number of girls as boys. Possibly something to do with the water. The Spartans were a warrior race, always at war with someone and, although they valued women for “companionship” and for making their sandwiches, they nevertheless needed more boys to join their army and replace soldiers killed in battle. The army was all male, and boys joined the army for training at the age of ten. The city elders decided to do something about this problem. They passed a law that, whilst families could have as many children as they wanted and whenever they wanted, as soon as a woman gave birth to a girl, she would be given a potion that would prevent her from bearing any more children. Assuming that the birthrate pattern continued, what was likely to be the ratio of boys to girls after exactly ten years?
Well, “Spartan born, Spartan bred. Strong in the arm, weak in the head”. The Spartans were fierce warriors but also incredibly stupid. The result of this law was that each year half the women were taken out of the breeding pool but the rest still produced the same ratio of boys to girls. Therefore after ten years the ratio of boys to girls would still be 50/50, but there would be far fewer boys for the army. Hardly surprising that Sparta is not a world power today.
And this month, while we are in Greece, one of its ancient philosophers asked “What is broken if you speak its name?”.