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Transylvanian Lottery
In mathematical combinatorics, the Transylvanian lottery is a lottery where three numbers between 1 and 14, inclusive, are picked by the player for any given ticket, and three numbers are chosen randomly. The player wins if two of their numbers, on a given ticket, are among the random ones. The problem of how many tickets the player must buy in order to be certain of winning can be solved by the use of the Fano plane. The solution is to buy a total of 14 tickets, in two sets of seven. One set of seven is every line of a Fano plane with the numbers 1 to 7, the other with 8 to 14: Because at least two of the winning numbers must be either high (8 to 14) or low (1 to 7), and every high and low pair is represented by exactly one ticket, at least two correct numbers are guaranteed to appear on one ticket with these 14 purchases. 21/26 of the time, the player will have only one ticket with only two numbers matched. If all three winning numbers are either high or low, the player wou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fano Plane Lottery
Fano is a town and ''comune'' of the province of Pesaro and Urbino in the Marche region of Italy. It is a beach resort southeast of Pesaro, located where the ''Via Flaminia'' reaches the Adriatic Sea. It is the third city in the region by population after Ancona and Pesaro. History An ancient town of Marche, it was known as Fanum Fortunae after a temple of Fortuna located there. Its first mention in history dates from 49 BC, when Julius Caesar held it, along with Pisaurum and Ancona. Caesar Augustus established a '' colonia'', and built a wall, some parts of which remain. In 2 AD Augustus also built an arch (which is still standing) at the entrance to the town. In January 271, the Roman Army defeated the Alamanni in the Battle of Fano that took place on the banks of the Metauro river just inland of Fano. Fano was destroyed by Vitiges' Ostrogoths in AD 538. It was rebuilt by the Byzantines, becoming the capital of the maritime Pentapolis ("Five Cities") that included al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lottery
A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments. The most common regulation is prohibition of sale to minors, and vendors must be licensed to sell lottery tickets. Although lotteries were common in the United States and some other countries during the 19th century, by the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in the U.S. and most of Europe as well as many other countries. This remained so until well after World War II. In the 1960s, casinos and lotteries began to re-appear throughout the world as a means for governments to raise revenue without raising taxes. Lotteries come in many formats. For example, the prize can be a fixed amount of cash or goods. In this format, there is risk t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fano Plane
In finite geometry, the Fano plane (after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. These points and lines cannot exist with this pattern of incidences in Euclidean geometry, but they can be given coordinates using the finite field with two elements. The standard notation for this plane, as a member of a family of projective spaces, is . Here stands for "projective geometry", the first parameter is the geometric dimension (it is a plane, of dimension 2) and the second parameter is the order (the number of points per line, minus one). The Fano plane is an example of a finite incidence structure, so many of its properties can be established using combinatorial techniques and other tools used in the study of incidence geometries. Since it is a projective space, algebraic techniques can also be effective tools in its study. Homogeneous coordinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of ''balance'' and/or ''symmetry''. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids. Combinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking, g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lottery Wheeling
Lottery wheeling (also known as lottery system, lottery wheel, lottery wheeling system) is an entertaining strategy of playing the lotteries, widely used by individual players and syndicates to secure wins provided they hit some of the drawn numbers. It allows playing with more than one ticket and more numbers than those drawn in the lottery. If the lottery is pick 6, then a wheeling system can be used in playing with 7 or more numbers. If the lottery is pick 5, then a wheeling system can be used in playing with 6 or more numbers. For example, in a pick 5 lottery, a lottery system can have 9 numbers and a guarantee of 3 if 3, meaning that the player will get a 3-win whenever three of his/her 9 numbers are among the five numbers drawn. In a pick 6 lottery, an example will be a system with, say, 12 numbers and a guarantee of 4 if 5, meaning that the player will get a 4-win whenever five of his/her 12 numbers are among the six numbers drawn. A lottery wheeling system acts as a single ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the '' American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Mission and Vision The mission of the MAA is to advance the understanding of mathematics and its impact on our world. We envision a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
