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## Riddles and Brain Teasers

Brainteaser is a problem in the form of a riddle. Solving such problems normally requires a lot of conventional thinking. Sometimes riddles and brain teasers really require ‘out of the box’ thinking.

Brain teasers often tease the human mind for its faulty reasoning, especially in problems of conditional probability. The conventional mind treats it as a problem of absolute probability. The difficulty one experiences in solving a brain teaser is a function of such thinking. An example of such thinking is well illustrated in this problem:

Someone has two children. Given that at least one of them is a boy, what is the probability that the other child would also be a boy? Simpler minds would think they are being asked to find the absolute probability of the second child being a boy. Since the probability of being a boy or girl is equal, the answer they would give is ½, which, as will be shown, is wrong.

For any couple with two children there are only 4 possibilities, considering that the probability of birth of a boy or a girl is same. These are:

1. 2 boys
2. 2 girls
3. first boy then girl
4. first girl then boy

Since in this problem, at least one is a boy, the second possibility ie. 2 girls, is eliminated. So there are just 3 possibilities out of which we are interested only in the first event, which is two boys. The correct answer is therefore 1/3. This approach avoids the error in the first approach in treating the births of the two children as independent events in all the 4 possibilities. In the correct approach once a girl is born first, the probability of a second girl being born is nil. Put differently, the probability of a second child being a girl or a boy is equal only when the first child is a boy.

Brain teasers have become a popular way of passing time among people of all ages. It is now becoming a necessary event in many parties or social gatherings since they enliven the proceedings. It has been seen that even the snooty, aloof types fall a prey to its seductive appeal to the brain. There are now brain teasers of all kinds to suit all tastes and styles with varying degrees of difficulty. There are the simpler ones which take a few minutes to solve and there are the complicated ones taking hours to solve. Many parties thrown by the fans of brain teasers have acquired certain fame only for their brain teaser party games. Next time you throw a party make sure to include brain teaser games.

Mental exercises like brainteasers are a good thing anywhere even in parties, especially those where things sometimes get out of hand. Intelligent hosts by including such riddles and brain teasers in their parties could perhaps make such get-togethers les rowdy than they normally are.