- Brain teaser
A

**brain teaser**is a form ofpuzzle that involves a lot of cogitating or mental/cognitive activity to solve. Normally, this includes thinking in conventional ways with given constraints in mind; sometimes, it also involves lateral thinking.Logic puzzle s andriddle s are specific types of brain teasers.One of the earliest known brain teaser enthusiasts was the Greek mathematician

Archimedes . [*cite book |last= |first= |authorlink= |coauthors=Editos of time-Life books, Inc. |title=The Puzzle Master |year=1989 |publisher=Time-Life Books |location=Alexandria, Virginia, USA |isbn=0809709287 |pages=18*] He devisedmathematical problem s for his peers to solve.**Example**:Q: "If three hens lay three eggs in three

day s, how many eggs does a hen lay in one day?"

:A1: "One third." (Note: 3 hens = 3 eggs / 3 days → 3 hens = (3 / 3) (eggs / days) → 1 hen = (1 / 3) (egg / days)):A2: "Zero or one" (it's hard to lay a third of an egg).It is easy for people to argue about the answers of many brain teasers; in the given example with hens, one might claim that all the eggs in the question were laid in the first day, so the answer would be three.

:Q: "Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, 4. Nono. What is the name of the fifth daughter?":A: "Mary. The first four daughters all have names with the first 4 vowels, so if someone does not think about the question, they may say the name with the fifth vowel, Nunu. The answer was given at the beginning of the question."

**Intuition**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 suchproblem s, the most famous probably being theMonty Hall problem . Another (simpler) example of such a brain teaser is given here::If we encounter someone with exactly two children, given that at least one of them is a boy, what is the probability that both of her children are boys?

(For simplicity, assume that boys and girls are born with equal probability.) The common intuitive way of thinking is that the births of the two children are independent of each other, and so the answer must be the absolute probability of one child being a boy, 1/2. However, the correct answer is

**1/3**as shown by the following argument:

*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**.Alternatively, one can see that in any sample of families with two children, 3/4 of them will have at least one son, and 1/4 will have two sons. The probability is thus (1/4)/(3/4) = 1/3. The common intuitive way of thinking is equivalent to considering families in which a "particular" child (e.g. the first-born, or the one that comes first in the alphabet, etc.) is a son (which is only 1/2 of the sample, not 3/4) and seeing how many of them have two sons.

One might formulate the above as: If someone has two children, and one of them is a son, what is the probability that the other is also a son?but that would be (more) ambiguous, since it could mean that we chose a person at random, and learnt that at least one of their two children was a son (in which case we get 1/3), or it could mean that we chose a person at random, and met one of their children, which turned out to be a son. This would then be a particular child, so the probability of the other being a son is 1/2.

The difference lies in the specific choice of words: The first example is considering the probability of a family having two sons in a row, if at least one of them is a son already (as shown in the proof). The second example might be understood to only ask for the sex of the second child, which is, given an even distribution of children born to each gender, one half or 1/2 either way.

**See also***

Board game

*List of puzzle video games

*Mathematical game

* Mensa

*Mind sport

*Boy or Girl paradox **References****External links*** – An active listing of links to brain teasers.

* [*http://mathdl.maa.org/convergence/1/?pa=content&sa=browseNode&categoryId=9 Historical Math Problems/Puzzles*] at [*http://mathdl.maa.org/convergence/1/ Convergence*]

*Wikimedia Foundation.
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### Look at other dictionaries:

**brain teaser**— brain teasers also brain teaser N COUNT A brain teaser is a question, problem, or puzzle that is difficult to answer or solve, but is not serious or important. Syn: puzzle, riddle … English dictionary**brain teaser**— UK US noun [countable] [singular brain teaser plural brain teasers] a difficult question or problem that you try to solve for fun Thesaurus: quizzes, puzzles and guessing gameshyponym to perform an act … Useful english dictionary**brain-teaser**— rain teaser n. a difficult problem. Syn: riddle, conundrum, enigma. [WordNet 1.5] … The Collaborative International Dictionary of English**brain teaser**— brain .teaser n a difficult problem that is fun trying to solve … Dictionary of contemporary English**brain-teaser**— ► NOUN informal ▪ a problem or puzzle … English terms dictionary**Brain Teaser**— Infobox roller coaster name = Brain Teaser caption = The Brain Teaser with the Mind Eraser in the background. location = Darien Lake type = Steel manufacturer = Zierer designer = Werner Stengel model = Out and Back roller coaster status = Open… … Wikipedia**brain-teaser**— noun a difficult problem • Syn: ↑riddle, ↑conundrum, ↑enigma • Derivationally related forms: ↑riddle (for: ↑riddle) • Hypernyms: ↑ … Useful english dictionary**brain teaser**— UK / US noun [countable] Word forms brain teaser : singular brain teaser plural brain teasers a difficult question or problem that you try to solve for fun … English dictionary**brain-teaser**— see brain teaser … English dictionary**brain teaser**— brain teas|er [ breın ,tizər ] noun count a difficult question or problem that you try to solve for fun … Usage of the words and phrases in modern English