In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m at least one container must contain more than one item. This theorem is exemplified in real life by truisms like "in any group of three gloves there must be at least two left gloves or at least two right gloves", it is an example of a counting argument. This obvious statement can be used to demonstrate unexpected results; the first formalization of the idea is believed to have been made by Peter Gustav Lejeune Dirichlet in 1834 under the name Schubfachprinzip. For this reason it is commonly called Dirichlet's box principle or Dirichlet's drawer principle; the principle can be stated in various ways. In a more quantified version: for natural numbers k and m, if n = k m + 1 objects are distributed among m sets the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects. For arbitrary n and m this generalizes to k + 1 = ⌊ / m ⌋ + 1 = ⌈ n / m ⌉, where ⌊ ⋯ ⌋ and ⌈ ⋯ ⌉ denote the floor and ceiling functions, respectively.
Though the most straightforward application is to finite sets, it is used with infinite sets that cannot be put into one-to-one correspondence. To do so requires the formal statement of the pigeonhole principle, "there does not exist an injective function whose codomain is smaller than its domain". Advanced mathematical proofs like Siegel's lemma build upon this more general concept. Dirichlet published his works in both French and German, using either the German Schubfach, or the French tiroir; the strict original meaning of both corresponds to the English drawer, an open-topped box that can be slid in and out of the cabinet that contains it. These terms were morphed to the word pigeonhole, standing for a small open space in a desk, cabinet, or wall for keeping letters or papers, metaphorically rooted in the structures that house pigeons. Since Dirichlet's father was a postmaster, furniture with pigeonholes is used for storing or sorting things into many categories, the translation pigeonhole may be a perfect rendering of Dirichlet's metaphor.
That understanding of the word, referring to some furniture features, is fading —especially among those who do not speak English natively but as a lingua franca in the scientific world— in favour of the more pictorial interpretation involving pigeons and holes. The suggestive, though not misleading interpretation of "pigeonhole" as "dovecote" has found its way back to a German back-translation of the "pigeonhole"-principle as the "Taubenschlag"-principle. Besides the original terms "Schubfach-Prinzip" in German and "Principe des tiroirs" in French, other literal translations are still in use in Polish, Turkish, Italian, Danish, Persian and Japanese. Assume a drawer contains a mixture of black socks and blue socks, each of which can be worn on either foot, that you are pulling a number of socks from the drawer without looking. What is the minimum number of pulled socks required to guarantee a pair of the same color? Using the pigeonhole principle, to have at least one pair of the same color using one pigeonhole per color, you need to pull only three socks from the drawer.
Either you have three of one color. If there are n people who can shake hands with one another, the pigeonhole principle shows that there is always a pair of people who will shake hands with the same number of people. In this application of the principle, the'hole' to which a person is assigned is the number of hands shaken by that person. Since each person shakes hands with some number of people from 0 to n − 1, there are n possible holes. On the other hand, either the'0' hole or the'n − 1' hole or both must be empty, for it is impossible for some person to shake hands with everybody else while some person shakes hands with nobody; this leaves n people to be placed into at most n − 1 non-empty holes. We can demonstrate there must be at least two people in London with the same number of hairs on their heads as follows. Since a typical human head has an average of around 150,000 hairs, it is reasonable to assume that no one has more than 1,000,000 hairs on their head. There are more than 1,000,000 people in London.
Assigning a pigeonhole to each number of hairs on a person's hea
Spin the bottle
Spin the bottle is a party game in which several players sit, stand, or kneel in a circle. A bottle is placed on the floor in the center of the circle. A player spins the bottle, must kiss the person to whom the bottle points when it stops spinning, it is popular among teenagers in the United States. There are a large number of variants. One variant is that instead, two players must hug within 5 seconds, they have to kiss in 10 seconds and if the 10 seconds are up and they haven't kissed, they have to French kiss. Variations allow for other tasks to be accomplished, it can be used to decide the player for another game such as Truth or Dare? Certain variations include penalties. Though it might be played by young teenagers or young adults, its fortune has declined starting from the 1980s. Spin the bottle was popular among teenagers over the second half of the 20th century because it fostered "sexual" interactions between boys and girls, it has been described as "the party game of choice for glandularly excited high schoolers".
The exact origin of this game is unknown though it seems reasonable that the game was invented in the United States no earlier than the first half of the 20th century. The earliest known written record of this game dates back to 1925. Written records of a similar game, called Bottle of Fortune, are available dating back to 1922. Seven minutes in heaven
Chinese whispers or telephone is an internationally popular children's game in which players form a line, the first player comes up with a message and whispers it to the ear of the second person in the line. The second player repeats the message to the third player, so on; when the last player is reached, they announce the message. The first person compares the original message with the final version. Although the objective is to pass around the message without it becoming garbled along the way, part of the enjoyment is that, this ends up happening. Errors accumulate in the retellings, so the statement announced by the last player differs from that of the first player with amusing or humorous effect. Reasons for changes include anxiousness or impatience, erroneous corrections, the difficult-to-understand mechanism of whispering, that some players may deliberately alter what is being said to guarantee a changed message by the end of the line; the game is played by children as a party game or on the playground.
It is invoked as a metaphor for cumulative error the inaccuracies as rumours or gossip spread, or, more for the unreliability of human recollection or oral traditions. As the game is popular among children worldwide, it is known under various other names depending on locality, such as Russian scandal, whisper down the lane, broken telephone, grapevine, don't drink the milk, secret message, the messenger game, pass the message among others. In France, it is called téléphone téléphone sans fil. In Malaysia, this game is referred to as telefon rosak, in Greece as spazmeno tilefono which both translate to broken telephone. In the United States, the game is known under the name telephone – which in this use is never shortened to the colloquial and more common word phone. Historians trace Westerners' use of the word Chinese to denote "confusion" and "incomprehensibility" to the earliest contacts between Europeans and Chinese people in the 17th century, attribute it to Europeans' inability to understand China's culture and worldview.
Using the phrase "Chinese whispers" suggested a belief that the Chinese language itself is not understandable. Additionally Chinese people have been stereotyped by Westerners as secretive or inscrutable; the more fundamental metonymic use of the name of a foreign language to represent a broader class of situations involving foreign languages or difficulty of understanding a language is captured in older idioms, such as "It's all Greek to me". The game has no winner: the entertainment comes from comparing the original and final messages. Intermediate messages may be compared; as well as providing amusement, the game can have educational value. It shows how information can become corrupted by indirect communication; the game has been used in schools to simulate the spread of its supposed harmful effects. It can be used to teach young children to moderate the volume of their voice, how to listen attentively, it can be used for older or adult learners of a foreign language, where the challenge of speaking comprehensibly, understanding, is more difficult because of the low volume, hence a greater mastery of the fine points of pronunciation is required.
A variant of Chinese whispers is called Rumors. In this version of the game, when players transfer the message, they deliberately change one or two words of the phrase. Intermediate messages can be compared. What an individual player changes in the message says something about the player; the pen-and-paper game Telephone Pictionary is played by alternately writing and illustrating captions, the paper being folded so that each player can only see the previous participant's contribution. Commercial boardgame versions Telestrations and Cranium Scribblish were both released in 2009; the game has been implemented online at Broken Picture Telephone and other sites. A translation relay is a variant in which the first player produces a text in a given language, together with a basic guide to understanding, which includes a lexicon, an interlinear gloss a list of grammatical morphemes, comments on the meaning of difficult words, etc.. The text is passed on to the following player, who tries to make sense of it and casts it into his/her language of choice repeating the procedure, so on.
Each player only knows the translation done by his immediate predecessor, but customarily the relay master or mistress collects all of them. The relay ends; the game has been played in the conlang community. Another variant of Chinese whispers is shown on Ellen's Game of Games under the name of Say Whaaaat?. However, the differences is that the 4 players will be wearing earphones, therefore the players have to read their lips. Drawception Epistemology Mondegreen Pavement radio Rumor Snowball effect Generation loss Exquisite corpse Broken Picture Telephone, an online game based on Chinese Whispers. Drawception, another online game which uses the concept. Chinese explains the game and offers some examples. Gossip and the Two-Part Telephone Game Global Gossip Game, a game of Gossip that passes from library t
Apple bobbing known as bobbing for apples, is a game played on Halloween. The game is played by putting apples in the water; because apples are less dense than water, they will float at the surface. Players try to catch one with their teeth. Use of arms is not allowed, are tied behind the back to prevent cheating. In Scotland, this may be called "dooking". In northern England, the game is called apple ducking or duck-apple. In Ireland County Kerry, it is known as "Snap Apple", in Newfoundland and Labrador, "Snap Apple Night" is a synonym for Halloween; the tradition of bobbing for apples dates back to the Roman invasion of Britain, when the conquering army merged their own celebrations with traditional Celtic festivals. The Romans brought with them a representation of the goddess of plenty, Pomona. During an annual celebration, young unmarried people try to bite into an apple floating in water or hanging from a string on a line, rather than in a bowl of water; the custom is mentioned in 18th century Ireland by Charles Vallancey in his book Collectanea de Rebus Hibernicis.
A maiden who placed the apple she bobbed under her pillow was said to dream of her future sweetheart. Agatha Christie's mystery novel Hallowe'en Party, is about a girl, drowned in an apple-bobbing tub. Snap-dragon
Ye Olde Trip to Jerusalem
Ye Olde Trip to Jerusalem is a public house in Nottingham which claims to have been established in 1189. The building rests against Castle Rock, upon which Nottingham Castle is built, is attached to several caves, carved out of the soft sandstone; these were reputedly used as a brewhouse for the castle, dating from the medieval period. The earliest known reference to the name "Ye Olde Trip to Jerusalem" was in 1799. Before being known by its current name, it is believed that the pub was named "The Pilgrim" and references to this name date back to 1751; the current name is believed to come from the belief that pilgrims or crusaders would stop at the inn on their journey to Jerusalem. Many elements of the pub's name are misunderstood in the modern day. Locals use a shortened version of the name, "the trip". Ye Olde Trip to Jerusalem is one of several pubs claiming to be the oldest in England - other pubs which claim to be the oldest include Ye Olde Salutation Inn and The Bell Inn in Nottingham, Ye Olde Fighting Cocks in St Albans, north of London.
The pub claims that it was established in 1189 AD - the year that Richard the Lionheart became king and Pope Gregory VIII called for a Third Crusade to the Holy Land. Evidence suggests that caves in the rock against which the pub is built were used as a brewhouse for Nottingham Castle, may date from around the time the castle was built in 1067; the oldest parts of the current building were constructed between 1650 and 1660, though a map by John Speed shows a previous building in existence in 1610. By 1751 the building was being used as an inn with the name The Pilgrim, was shortly after that date purchased by William Standford; the first record of the use of the name Ye Olde Trip to Jerusalem dates from 1799. Brew House Yard acquired its name after 1680. Official website
Pin the tail on the donkey
Pin the tail on the donkey is a game played by groups of children. The earliest version listed in a catalog of American games compiled by the American Game Collectors Association in 1998, is dated 1899, attributed to Charles Zimmerling, it is common at other gatherings. A picture of a donkey with a missing tail is tacked to a wall within easy reach of children. One at a time, each child is blindfolded and handed a paper "tail" with a push pin or thumbtack poked through it; the blindfolded child is spun around until he or she is disoriented. The child tries to pin the tail on the donkey; the player who pins their tail closest to the target, the donkey's rear, wins. The game, a group activity, is not competitive, it is seen as more entertaining, seeing the children stumble around and try to put their tail at the right place. The game is used in child development research; the game can be played by teenagers and adults if the "donkey" is replaced with depictions of something or someone else. As a drinking game, the person with the worst tail pinning is awarded one shot of a selected alcohol, to be determined by house rules or the loser in a friendly environment.
Idiomatically, the term can be used derisively for any assigned activity, pointless or for which a person has been handicapped. Eeyore, a character who loses his tail and has to have it pinned back on. Fukuwarai, a similar Japanese game Piñata Printable Pin the Tail on the Donkey Game
Twenty Questions is a spoken parlor game which encourages deductive reasoning and creativity. It originated in the United States and was played in the 19th century, it escalated in popularity during the late 1940s when it became the format for a successful weekly radio quiz program. In the traditional game, one player is chosen to be the answerer; that person does not reveal this to the others. All other players are questioners, they each take turns asking a question which can be answered with a simple "Yes" or "No." In variants of the game, multiple state answers may be included such as the answer "Maybe." The answerer answers each question in turn. Sample questions could be: "Is it bigger than a breadbox?" or "Can I put it in my mouth?" Lying is not allowed in the game. If a questioner guesses the correct answer, that questioner wins and becomes the answerer for the next round. If 20 questions are asked without a correct guess the answerer has stumped the questioners and gets to be the answerer for another round.
Careful selection of questions can improve the odds of the questioner winning the game. For example, a question such as "Does it involve technology for communications, entertainment or work?" can allow the questioner to cover a broad range of areas using a single question that can be answered with a simple "yes" or "no". If the answerer responds with "yes," the questioner can use the next question to narrow down the answer; the most popular variant is called "Animal, Mineral." This is taken from the Linnaean taxonomy of the natural world. In this version, the answerer tells the questioners at the start of the game whether the subject belongs to the animal, vegetable or mineral kingdom; these categories can produce odd technicalities, such as a wooden table being classified as a vegetable, or a belt being both animal and mineral, or vegetable, if made from plant fibers. Other versions specify that the item to be guessed should be in a given category, such as actions, famous people, etc. In Hungary, a similar game is named after Simon bar Kokhba.
A version of Twenty Questions called Yes and No is played as a parlour game by characters of Charles Dickens' A Christmas Carol. Similar to the aforementioned, there is another version known to English as a Second Language educators, played based on a given topic. There are many different ways. 20 Questions on "Educate, Learn", for example, was developed for the Austrian Federal Ministry of Education and Women's Affairs. The abstract mathematical version of the game where some answers may be wrong is sometimes called Ulam's game or the Rényi–Ulam game; the game suggests. The game is used as an example when teaching people about information theory. Mathematically, if each question is structured to eliminate half the objects, 20 questions will allow the questioner to distinguish between 220 or 1,048,576 objects. Accordingly, the most effective strategy for Twenty Questions is to ask questions that will split the field of remaining possibilities in half each time; the process is analogous to a binary search algorithm in computer science or successive approximation ADC in analog-to-digital signal conversion.
In 1901 Charles Sanders Peirce discussed factors in the economy of research that govern the selection of a hypothesis for trial — cheapness, intrinsic value, relation to other projects. He discussed the potential of Twenty Questions to single one subject out from among 220 and, pointing to skillful caution, Thus twenty skillful hypotheses will ascertain what two hundred thousand stupid ones might fail to do; the secret of the business lies in the caution which breaks a hypothesis up into its smallest logical components, only risks one of them at a time. He elaborated on how, if that principle had been followed in the investigation of light, its investigators would have saved themselves from half a century of work. Note that testing the smallest logical components of a hypothesis one at a time does not mean asking about, say, 1,048,576 subjects one at a time. Instead it means extracting aspects of a guess or hypothesis, asking, for example, "did an animal do this?" before asking "did a horse do this?".
That aspect of scientific method resembles a situation puzzle in facing a puzzling scenario at the start. Both games involve asking yes/no questions, but Twenty Questions places a greater premium on efficiency of questioning. A limit on their likeness to the scientific process of trying hypotheses is that a hypothesis, because of its scope, can be harder to test for truth than to test for falsity or vice versa. In developing the Participatory Anthropic Principle, an interpretation of quantum mechanics, theoretical physicist John Archibald Wheeler used a variant on Twenty Questions, called Negative Twenty Questions, to show how the questions we choose to ask about the universe may dictate the answers we get. In this variant, the respondent does not choose or decide upon any particular or definite object beforehand, but only on a pattern of'Yes' or'No' answers; this variant requires the respondent to provide a consistent set of answers to successiv