Problem: Following this battle, Ali fought a battle against Muawiyah, known as the Battle of Siffin. The battle was stopped before either side had achieved victory, and the two parties agreed to arbitrate their dispute. After the battle Amr ibn al-As was appointed by Muawiyah as an arbitrator, and Ali appointed Abu Musa Ashaari. Seven months later, in February 658, the two arbitrators met at Adhruh, about 10 miles north west of Maan in Jordon. Amr ibn al-As convinced Abu Musa Ashaari that both Ali and Muawiyah should step down and a new Caliph be elected. Ali and his supporters were stunned by the decision which had lowered the Caliph to the status of the rebellious Muawiyah I. Ali was therefore outwitted by Muawiyah and Amr. Ali refused to accept the verdict and found himself technically in breach of his pledge to abide by the arbitration. This put Ali in a weak position even amongst his own supporters. The most vociferous opponents in Ali's camp were the very same people who had forced Ali into the ceasefire. They broke away from Ali's force, rallying under the slogan, "arbitration belongs to God alone." This group came to be known as the Kharijites ("those who leave"). In 659 Ali's forces and the Kharijites met in the Battle of Nahrawan. Although Ali won the battle, the constant conflict had begun to affect his standing, and in the following years some Syrians seem to have acclaimed Muawiyah as a rival caliph.
What group's name means "those who stay"?
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Answer: unanswerable

Problem: 1855: Georgian coast: Omar Pasha, the Turkish commander at Crimea had long wanted to land in Georgia, but the western powers vetoed it. When they relented in August most of the campaigning season was lost. In September 8000 Turks landed at Batum, but the main concentration was at Sukhum Kale. This required a 100-mile march south through a country with poor roads. The Russians planned to hold the line of the Ingur River which separates Abkhazia from Georgia proper. Omar crossed the Ingur on 7 November and then wasted a great deal of time, the Russians doing little. By 2 December he had reached the Tskhenis-dzqali, the rainy season had started, his camps were submerged in mud and there was no bread. Learning of the fall of Kars he withdrew to the Ingur. The Russians did nothing and he evacuated to Batum in February of the following year.
What did Omar Pasha finally reach on December 2nd 1855?
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Answer: the Tskhenis-dzqali

Problem: In the example above, the identity and the rotations constitute a subgroup R = {id, r1, r2, r3}, highlighted in red in the group table above: any two rotations composed are still a rotation, and a rotation can be undone by (i.e. is inverse to) the complementary rotations 270 for 90, 180 for 180, and 90 for 270 (note that rotation in the opposite direction is not defined). The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g1h H for all elements g, h H. Knowing the subgroups is important in understanding the group as a whole.d["]
270 for 180 is an example of what kind of rotation?
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Answer:
unanswerable