Brain teasers are a form of puzzle that involve a lot of thinking (mental/cognitive activity). Normally, this includes thinking in conventional ways with given constraints in mind; sometimes, it also involves lateral thinking.
Example:
- Q: If three hens lay three eggs in three days, how many eggs does a hen lay in one day?
- A: One third. (Note: 3 hens = 3 eggs / 3 days → 3 hens = (3 / 3) (eggs / days) → 1 hen = (1 / 3) (egg / days))
The difficulty of many brain teasers relies on a certain degree of fallacy in human intuitiveness. This is most common in brain teasers relating to conditional probability, because the casual human mind tends to consider absolute probability instead. As a result, a great number of controversial discussions emerge from such problems, the most famous probably being the Monty Hall problem. Another (simpler) example of such a brain teaser is given here:
- If we encounter someone with two children, given that at least one of them is a son, what is the probability that the other is also a son?
- For a single birth, there are two possibilities (a boy or a girl) with equal probability.
- Therefore, for two births, there are four possibilities: 1) two boys, 2) two girls, 3) first a boy, then a girl, and 4) first a girl, then a boy; all of them have equal probability.
- We are given that one of the children is a boy. Thus, only one of the four possibilities -- two daughters -- is eliminated. Three possibilities with equal probabilities (1/3) remain.
- Out of those three, only one -- two sons -- is what we are looking for. Hence, the answer is 1/3.
- If someone has two children, and one of them is a son, what is the probability that the other is also a son?