Problem: Group (mathematics):

The modern concept of an abstract group developed out of several fields of mathematics. The original motivation for group theory was the quest for solutions of polynomial equations of degree higher than 4. The 19th-century French mathematician Évariste Galois, extending prior work of Paolo Ruffini and Joseph-Louis Lagrange, gave a criterion for the solvability of a particular polynomial equation in terms of the symmetry group of its roots (solutions). The elements of such a Galois group correspond to certain permutations of the roots. At first, Galois' ideas were rejected by his contemporaries, and published only posthumously. More general permutation groups were investigated in particular by Augustin Louis Cauchy. Arthur Cayley's On the theory of groups, as depending on the symbolic equation θn = 1 (1854) gives the first abstract definition of a finite group.

When did Arthur Cayley publish On the theory of groups?
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A: unanswerable


Problem: North Carolina:

After the Spanish in the 16th century, the first permanent European settlers of North Carolina were English colonists who migrated south from Virginia. The latter had grown rapidly and land was less available. Nathaniel Batts was documented as one of the first of these Virginian migrants. He settled south of the Chowan River and east of the Great Dismal Swamp in 1655. By 1663, this northeastern area of the Province of Carolina, known as the Albemarle Settlements, was undergoing full-scale English settlement. During the same period, the English monarch Charles II gave the province to the Lords Proprietors, a group of noblemen who had helped restore Charles to the throne in 1660. The new province of "Carolina" was named in honor and memory of King Charles I (Latin: Carolus). In 1712, North Carolina became a separate colony. Except for the Earl Granville holdings, it became a royal colony seventeen years later. A large revolt happened in the state in 1711 known as Cary's Rebellion.

What year did Nathaniel Battes settle in North Carolina?
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A: 1655


Problem: IBM:

Thomas J. Watson, Sr., fired from the National Cash Register Company by John Henry Patterson, called on Flint and, in 1914, was offered CTR. Watson joined CTR as General Manager then, 11 months later, was made President when court cases relating to his time at NCR were resolved. Having learned Patterson's pioneering business practices, Watson proceeded to put the stamp of NCR onto CTR's companies. He implemented sales conventions, "generous sales incentives, a focus on customer service, an insistence on well-groomed, dark-suited salesmen and had an evangelical fervor for instilling company pride and loyalty in every worker". His favorite slogan, "THINK", became a mantra for each company's employees. During Watson's first four years, revenues more than doubled to $9 million and the company's operations expanded to Europe, South America, Asia and Australia. "Watson had never liked the clumsy hyphenated title of the CTR" and chose to replace it with the more expansive title "International Business Machines". First as a name for a 1917 Canadian subsidiary, then as a line in advertisements. For example, the McClures magazine, v53, May 1921, has a full page ad with, at the bottom:

What happened to the revenue of the National Cash Register Company when Patterson became president?
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A: unanswerable


Problem: Pacific War:

Japan sponsored several puppet governments, one of which was headed by Wang Jingwei. However, its policies of brutality toward the Chinese population, of not yielding any real power to these regimes, and of supporting several rival governments failed to make any of them a viable alternative to the Nationalist government led by Chiang Kai-shek. Conflicts between Chinese communist and nationalist forces vying for territory control behind enemy lines culminated in a major armed clash in January 1941, effectively ending their co-operation.

Who was the leader of the Nationalist government?
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A:
Chiang Kai-shek