Problem: Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
What area of classification leads to troublesome arithmetic?
The answer is the following: finite groups


In addition to city government, numerous commissions and state authorities—including the Massachusetts Department of Conservation and Recreation, the Boston Public Health Commission, the Massachusetts Water Resources Authority (MWRA), and the Massachusetts Port Authority (Massport)—play a role in the life of Bostonians. As the capital of Massachusetts, Boston plays a major role in state politics.
What is the capital of Massachusetts?
Boston


Input: Atlantic City, New Jersey
In the city, 24.6% of the population were under the age of 18, 10.2% from 18 to 24, 26.8% from 25 to 44, 25.8% from 45 to 64, and 12.7% who were 65 years of age or older. The median age was 36.3 years. For every 100 females there were 96.2 males. For every 100 females age 18 and over, there were 94.4 males.

What was the median age?
Output: 36.3 years


Input: Article: Political and religious animosity against Jehovah's Witnesses has at times led to mob action and government oppression in various countries. Their doctrine of political neutrality and their refusal to serve in the military has led to imprisonment of members who refused conscription during World War II and at other times where national service has been compulsory. In 1933, there were approximately 20,000 Jehovah's Witnesses in Germany, of whom about 10,000 were later imprisoned. Of those, 2000 were sent to Nazi concentration camps, where they were identified by purple triangles; as many as 1200 died, including 250 who were executed. In Canada, Jehovah's Witnesses were interned in camps along with political dissidents and people of Chinese and Japanese descent. In the former Soviet Union, about 9,300 Jehovah's Witnesses were deported to Siberia as part of Operation North in April 1951. Their religious activities are currently banned or restricted in some countries, including China, Vietnam and some Islamic states.

Now answer this question: Of the 20,000 Jehovah's Witnesses in Germany in 1933, how many were later imprisoned?

Output: 10,000


Article: Over the course of Ottoman history, the Ottomans managed to build a large collection of libraries complete with translations of books from other cultures, as well as original manuscripts. A great part of this desire for local and foreign manuscripts arose in the 15th Century. Sultan Mehmet II ordered Georgios Amiroutzes, a Greek scholar from Trabzon, to translate and make available to Ottoman educational institutions the geography book of Ptolemy. Another example is Ali Qushji -an astronomer, mathematician and physicist originally from Samarkand- who became a professor in two madrasas, and influenced Ottoman circles as a result of his writings and the activities of his students, even though he only spent two or three years before his death in Istanbul.

Question: In what century did the Ottoman's start to desire foreign manuscripts?
Ans: 15th Century


Input: Zhejiang
Zhejiang is the home of Yueju (越劇), one of the most prominent forms of Chinese opera. Yueju originated in Shengzhou and is traditionally performed by actresses only, in both male and female roles. Other important opera traditions include Yongju (of Ningbo), Shaoju (of Shaoxing), Ouju (of Wenzhou), Wuju (of Jinhua), Taizhou Luantan (of Taizhou) and Zhuji Luantan (of Zhuji).

Where did Yueju originate?
Output:
Shengzhou