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Chopsticks (hand Game)
Chopsticks is a hand game for two or more players, in which players extend a number of fingers from each hand and transfer those scores by taking turns to tap one hand against another. Chopsticks is an example of a combinatorial game, and is solved in the sense that with perfect play, an optimal strategy from any point is known. Rules This official set of rules is called ''rollover'' where five fingers are subtracted should a hand's sum exceeds 5 as described below. # A hand is ''live'' if it has at least one finger, and this is indicated by raising at least one finger. If a hand has zero fingers, the hand is ''dead'', and this is indicated by raising zero fingers (i.e. a closed fist). # If any hand of any player reaches exactly five fingers, then the hand is dead. # Each player begins with one finger raised on each hand. After the first player turns proceed clockwise. # On a player's turn, they must either ''attack'' or ''split''. There are two types of splits, ''transfers'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hands As2 And 3
A hand is a prehensile, multi-fingered appendage located at the end of the forearm or forelimb of primates such as humans, chimpanzees, monkeys, and lemurs. A few other vertebrates such as the Koala#Characteristics and adaptations, koala (which has two thumb#Opposition and apposition, opposable thumbs on each "hand" and fingerprints extremely similar to human fingerprints) are often described as having "hands" instead of paws on their front limbs. The raccoon is usually described as having "hands" though opposable thumbs are lacking. Some evolutionary anatomists use the term ''hand'' to refer to the appendage of digits on the forelimb more generally—for example, in the context of whether the three Digit (anatomy), digits of the bird hand involved the same Homology (biology), homologous loss of two digits as in the dinosaur hand. The human hand usually has five digits: four fingers plus one thumb; these are often referred to collectively as five fingers, however, whereby the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trivial Group
In mathematics, a trivial group or zero group is a group consisting of a single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and so it is usually denoted as such: 0, 1, or e depending on the context. If the group operation is denoted \, \cdot \, then it is defined by e \cdot e = e. The similarly defined is also a group since its only element is its own inverse, and is hence the same as the trivial group. The trivial group is distinct from the empty set, which has no elements, hence lacks an identity element, and so cannot be a group. Definitions Given any group G, the group consisting of only the identity element is a subgroup of G, and, being the trivial group, is called the of G. The term, when referred to "G has no nontrivial proper subgroups" refers to the only subgroups of G being the trivial group \ and the group G itself. Properties The trivial group is cyclic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Strategy Games
Abstract strategy games admit a number of definitions which distinguish these from strategy games in general, mostly involving no or minimal narrative theme, outcomes determined only by player choice (with no randomness), and perfect information. For example, Go is a pure abstract strategy game since it fulfills all three criteria; chess and related games are nearly so but feature a recognizable theme of ancient warfare; and Stratego is borderline since it is deterministic, loosely based on 19th-century Napoleonic warfare, and features concealed information. Definition Combinatorial games have no randomizers such as dice, no simultaneous movement, nor hidden information. Some games that do have these elements are sometimes classified as abstract strategy games. (Games such as '' Continuo'', Octiles, '' Can't Stop'', and Sequence, could be considered abstract strategy games, despite having a luck or bluffing element.) A smaller category of abstract strategy games manages to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hand Games
Hand games are games played using only the hands of the players. Hand games exist in a variety of cultures internationally, and are of interest to academic studies in ethnomusicology and music education. Hand games are used to teach music literacy skills and socio-emotional learning in elementary music classrooms internationally. Examples of hand games * Chopsticks (sticks) * Clapping games * Mercy * Morra (finger counting) * Odds and evens * Pat-a-cake and variations: ** Mary Mack * Red hands (or hand-slap game) * Rock paper scissors * Thumb war (or thumb wrestling) * " Where are your keys?" (language acquisition game) Less strictly, the following may be considered hand games: * Bloody knuckles * Fingers (drinking game) * Jacks * Knife game * Spellbinder * Stick gambling * String games, such as cat's cradle Cat's cradle is a game involving the creation of various string figures between the fingers, either individually or by passing a loop of string back and fort ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Children's Games
This is a list of games that used to be played by children, some of which are still being played today. Traditional children's games do not include commercial products such as board games but do include games which require props such as hopscotch or marbles (toys go in List of toys unless the toys are used in multiple games or the single game played is named after the toy; thus "jump rope" is a game, while "Jacob's ladder" is a toy). Despite being transmitted primarily through word of mouth due to not being considered suitable for academic study or adult attention, traditional games have, "not only failed to disappear but have also evolved over time into new versions." Traditional children's games are defined, "as those that are played informally with minimal equipment, that children learn by example from other children, and that can be played without reference to written rules. These games are usually played by children between the ages of 7 and 12, with some latitude on both end ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morra (game)
Morra is a hand game that dates back thousands of years to ancient Roman and Greek times. Each player simultaneously reveals their hand, extending any number of fingers, and calls out a number. Any player who successfully guesses the total number of fingers revealed by all players combined scores a point. Morra can be played to decide issues, much as two people might toss a coin, or for entertainment. Rules While there are many variations of morra, most forms can be played with a minimum of two players. In the most popular version, all players throw out a single hand, each showing zero to five fingers, and call out their guess at what the sum of all fingers shown will be. If one player guesses the sum, that player earns one point. The first player to reach three points wins the game. Some variants of morra involve money, with the winner earning an amount equal to the sum of fingers displayed. History Morra was known to the ancient Romans and is popular around the world, es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer is divisible by a nonzero integer if there exists an integer such that n=km. This is written as :m\mid n. Other ways of saying the same thing are that divides , is a divisor of , is a factor of , and is a multiple of . If does not divide , then the notation is m\not\mid n. Usually, is required to be nonzero, but is allowed to be zero. With this convention, m \mid 0 for every nonzero integer . Some definitions omit the requirement that m be nonzero. General Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Applications of Fibonacci numbers include co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degeneracy (mathematics)
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class, and the term degeneracy is the condition of being a degenerate case. The definitions of many classes of composite or structured objects often implicitly include inequalities. For example, the angles and the side lengths of a triangle are supposed to be positive. The limiting cases, where one or several of these inequalities become equalities, are degeneracies. In the case of triangles, one has a ''degenerate triangle'' if at least one side length or angle is zero. Equivalently, it becomes a "line segment". Often, the degenerate cases are the exceptional cases where changes to the usual dimension or the cardinality of the object (or of some part of it) occur. For example, a triangle is an object of dimension two, and a degenerate triangle is contained in a line, which makes its dimension one. This is similar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero Game
In combinatorial game theory, the zero game is the game where neither player has any legal options. Therefore, under the normal play convention, the first player automatically loses, and it is a second-player win. The zero game has a Sprague–Grundy value of zero. The combinatorial notation of the zero game is: .. A zero game should be contrasted with the star game , which is a first-player win since either player must (if first to move in the game) move to a zero game, and therefore win. Examples Simple examples of zero games include Nim with no piles or a Hackenbush diagram with nothing drawn on it. Sprague-Grundy value The Sprague–Grundy theorem applies to impartial game In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference bet ...s (in which each move may be played by either pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hand Game
Hand games are games played using only the hands of the players. Hand games exist in a variety of cultures internationally, and are of interest to academic studies in ethnomusicology and music education. Hand games are used to teach music literacy skills and socio-emotional learning in elementary music classrooms internationally. Examples of hand games * Chopsticks (sticks) * Clapping games * Mercy * Morra (finger counting) * Odds and evens * Pat-a-cake and variations: ** Mary Mack * Red hands (or hand-slap game) * Rock paper scissors * Thumb war (or thumb wrestling) * " Where are your keys?" (language acquisition game) Less strictly, the following may be considered hand games: * Bloody knuckles * Fingers (drinking game) * Jacks * Knife game * Spellbinder * Stick gambling * String games, such as cat's cradle Cat's cradle is a game involving the creation of various string figures between the fingers, either individually or by passing a loop of string back and forth b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangular Number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in the triangular arrangement with dots on each side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers, starting with the 0th triangular number, is (This sequence is included in the On-Line Encyclopedia of Integer Sequences .) Formula The triangular numbers are given by the following explicit formulas: T_n= \sum_^n k = 1+2+3+ \dotsb +n = \frac = , where \textstyle is a binomial coefficient. It represents the number of distinct pairs that can be selected from objects, and it is read aloud as " plus one choose two". The first equation can be illustrated using a visual proof. For every triangular number T_n, imagine a "half-square" arrangement of objects corresponding to the triangular numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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