In this task, you're given passages that contain mentions of names of people, places, or things. Some of these mentions refer to the same person, place, or thing. Your job is to write questions that evaluate one's understanding of such references. Good questions are expected to link pronouns (she, her, him, his, their, etc.) or other mentions to people, places, or things to which they may refer. Do not ask questions that can be answered correctly without understanding the paragraph or having multiple answers. Avoid questions that do not link phrases referring to the same entity. For each of your questions, the answer should be one or more phrases in the paragraph, and it should be unambiguous.

Let me give you an example: Passage: Nearing London, Oliver encounters Jack Dawkins, a pickpocket more commonly known by the nickname the "Artful Dodger", and his sidekick, a boy of a humorous nature named Charley Bates, but Oliver's innocent and trusting nature fails to see any dishonesty in their actions. The Dodger provides Oliver with a free meal and tells him of a gentleman in London who will "give him lodgings for nothing, and never ask for change". Grateful for the unexpected assistance, Oliver follows the Dodger to the "old gentleman's" residence. In this way Oliver unwittingly falls in with an infamous Jewish criminal known as Fagin, the gentleman of whom the Artful Dodger spoke. Ensnared, Oliver lives with Fagin and his gang of juvenile pickpockets in their lair at Saffron Hill for some time, unaware of their criminal occupations. He believes they make wallets and handkerchiefs.
The answer to this example can be: Who believes Fagin's gang make wallets and handkerchiefs?.
Here is why: This question is based on the following sentence in the passage "He believes they make wallets and handkerchiefs". It evaluates the understanding that the pronoun "he" refers to name "Oliver". You can ask questions like this one about most pronouns in a paragraph.

OK. solve this:
Passage: Henry III's reign was in crisis in 1258. He had recently suffered defeat in Wales, there were agricultural problems leading to a famine, and relations with the pope were worsening. Discontent amongst England's magnates led Henry to promise reform, but under continued pressure his authority disintegrated. A royal council of fifteen magnates was formed in June that year, and the rule of the country transferred from the king to the council. With foreign help Henry's reign was restored in 1261 as the council were reluctant to start a civil war. Simon de Montfort, Earl of Leicester, raised a rebellion. In 1264 civil war broke out between those loyal to the king and the baronial forces led by de Montfort.Rochester's constable in 1264, Roger de Leybourne, held the castle in support of Henry. John de Warenne, Earl of Surrey, was the garrison's co-commander. A baronial army led by Gilbert de Clare, Earl of Hertford, laid siege to the castle on 17 April that year. Having marched from the earl's castle to Tonbridge the army attacked from the Rochester side of the river, either the south or west. While the army advanced towards the city the royalist garrison set alight the suburbs. The king's hall within the castle was also burned down, although it is unclear why. An army under Simon de Montfort marched from London with the intention of attacking the city from another direction. The earl's first two attempts to cross the Medway were fought back, but he was successful on 18 April, Good Friday. The method used is uncertain, although it involved a fire-ship. The smoke may have been used as cover for the rebels, or the ship may have been used to burn the bridge while the army travelled by water. In a co-ordinated attack that had been pre-arranged, the armies of de Montfort and de Clare attacked the city. They entered Rochester in the evening and that night the cathedral was raided. The following day the rebels captured the castle's outer enclosure and the royal garrison retreated to the keep. Because the next day was Easter Sunday there was no fighting, though hostilities resumed on the Monday. Siege engines were set up and targeted the keep. As in 1215 the keep proved resistant to missiles, and after a week had not succumbed. According to one contemporary source, the besiegers were about to dig a mine beneath the tower, but the siege was abandoned on 26 April when the earls received news of a relief force led by Henry III and his son, Prince Edward.
Answer:
What is the full name of the king whose hall within the castle also burned down?