Puzzle: A town in India contains 100,000 married couples but no children. Every one strongly believes in continuing the male line. On the other hand population is also a big problem.
So town's wise men decides:
1. Each family has one baby per annum until the first boy is born. For example, if (at some future date) a family has five children, then it must be either that they are all girls, and another child is planned, or that there are four girls and one boy, and no more children are planned.
2. Children are equally likely to be born male or female.
Let p(t) be the percentage of children that are male at the end of year t. How is this percentage expected to evolve through time?
Note: Don't forget to visit us again. Answer to the puzzle will be posted tomorrow.
Source: Nigel's puzzle page.
Solution: The strategy is to solve year by year and see the trend
1. 1st year: 50,000 boys, 50,000 girls.
2. 2nd year: 50,000 boys + 25,000 boys, 50,000 girls + 25000 girls.
3. 3rd year: 75000 boys + 12,500 boys, 50,000 girls + 12500 girls
and so on...
So it shows that it will always be 50%.
Winner: Kasturi is the winner.
Since every year equal number of boys and girls will be born, irrespective of the total number of children, the percentage of boys will always be 50%.
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