Problem: Group (mathematics):

This set inherits a group operation (sometimes called coset multiplication, or coset addition) from the original group G: (gN) • (hN) = (gh)N for all g and h in G. This definition is motivated by the idea (itself an instance of general structural considerations outlined above) that the map G → G / N that associates to any element g its coset gN be a group homomorphism, or by general abstract considerations called universal properties. The coset eN = N serves as the identity in this group, and the inverse of gN in the quotient group is (gN)−1 = (g−1)N.e[›]

What is another term for coset multiplication?
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A: coset addition


Problem: Exchanging "+" and "−" in the expression, i.e. permuting the two solutions of the equation can be viewed as a (very simple) group operation. Similar formulae are known for cubic and quartic equations, but do not exist in general for degree 5 and higher. Abstract properties of Galois groups associated with polynomials (in particular their solvability) give a criterion for polynomials that have all their solutions expressible by radicals, i.e. solutions expressible using solely addition, multiplication, and roots similar to the formula above.
Which group cannot be expressed using radicals?
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Answer: unanswerable


Q: What is a question about this article? If the question is unanswerable, say "unanswerable".
More than 200 newspapers and 350 consumer magazines have an office in the city, and the publishing industry employs about 25,000 people. Two of the three national daily newspapers in the United States are New York papers: The Wall Street Journal and The New York Times, which has won the most Pulitzer Prizes for journalism. Major tabloid newspapers in the city include: The New York Daily News, which was founded in 1919 by Joseph Medill Patterson and The New York Post, founded in 1801 by Alexander Hamilton. The city also has a comprehensive ethnic press, with 270 newspapers and magazines published in more than 40 languages. El Diario La Prensa is New York's largest Spanish-language daily and the oldest in the nation. The New York Amsterdam News, published in Harlem, is a prominent African American newspaper. The Village Voice is the largest alternative newspaper.
How many newspaper offices are located in New York?
A: More than 200


Context and question: Originally named the Institute of British Architects in London, it was formed in 1834 by several prominent architects, including Philip Hardwick, Thomas Allom, William Donthorne, Thomas Leverton Donaldson, William Adams Nicholson, John Buonarotti Papworth, and Thomas de Grey, 2nd Earl de Grey.
In what year was the Institute of British Architects founded?
Answer: 1834


Question: Compared to other team sports, the National Football League preseason is very structured. Every NFL team plays exactly four pre-season exhibition games a year, two at home and two away, with the exception of two teams each year who play a fifth game, the Pro Football Hall of Fame Game. These exhibition games, most of which are held in the month of August, are played for the purpose of helping coaches narrow down the roster from the offseason limit of 90 players to the regular-season limit of 53 players. While the scheduling formula is not as rigid for preseason games as they are for the regular season, there are numerous restrictions and traditions that limit the choices of preseason opponents; teams are also restricted on what days and times they can play these games. Split-squad games, a practice common in baseball and hockey, where a team that is scheduled to play two games on the same day splits their team into two squads, are prohibited. The NFL has played exhibition games in Europe, Japan, Canada, Australia (including the American Bowl in 1999) and Mexico to spread the league's popularity (a game of this type was proposed for China but, due to financial and logistical problems, was eventually canceled). The league has tacitly forbidden the playing of non-league opponents, with the last interleague game having come in 1972 and the last game against a team other than an NFL team (the all-NFL rookie College All-Stars) was held in 1976. Exhibition games are quite unpopular with many fans, who resent having to pay regular-season prices for two home exhibition games as part of a season-ticket package. Numerous lawsuits have been brought by fans and classes of fans against the NFL or its member teams regarding this practice, but none have been successful in halting it.[citation needed] The Pro Bowl, traditionally played after the end of the NFL season (since 2011 is played the week prior to the Super Bowl), is also considered an exhibition game.
Is there an answer to this question: What team sport has very unstructured preseason's?

Answer: unanswerable


Problem: PlayStation 3:

Sony officially unveiled PlayStation 3 (then marketed as PLAYSTATION 3) to the public on May 16, 2005, at E3 2005, along with a 'boomerang' shaped prototype design of the Sixaxis controller. A functional version of the system was not present there, nor at the Tokyo Game Show in September 2005, although demonstrations (such as Metal Gear Solid 4: Guns of the Patriots) were held at both events on software development kits and comparable personal computer hardware. Video footage based on the predicted PlayStation 3 specifications was also shown (notably a Final Fantasy VII tech demo).

What popular game was demoed in a video at the game shows?
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A:
Final Fantasy VII