Hard Answers

 is received right after the completion of Speaking With Silence.

Objectives

 * Speak with Enthir.
 * Speak with Calcelmo inside the Understone Keep in Markarth.
 * Gain Entry to Calcelmo's Museum.
 * (Optional) Obtain key to Calcelmo's Museum.
 * Find Calcelmo's Falmer Translating Guide.
 * Duplicate the writing on Calcelmo's Stone with charcoal and a paper roll.
 * Return to Enthir.
 * Speak to Karliah.

Walkthrough

 * Speak to Enthir at The Frozen Hearth in Winterhold or in The College of Winterhold.
 * Travel to Markarth and speak to Calcelmo at Understone Keep - He will not grant access to his research unless persuaded, bribed, or intimidated (or by helping him out by completing the temple quest The Book of Love), or by completing the side quest to kill the spider in the excavation site. It can also be pickpocketed from him.
 * Find (or receive through a side-quest from Calcelmo) the key to Calcelmo's Museum on his Alchemy table in the South wing of the Keep (where he must be found). It may also be on the small table next to the alchemy table.
 * Go to the North wing of the Keep and enter the Museum. If Nimhe has not been killed, then the guard at the door will tell the Dragonborn that they are not allowed to go in, after the dialogue the guard will allow entrance into the museum.
 * Enter the museum. If Nimhe has been killed, the guards will not be hostile. Otherwise, sneak past or kill the guards; having a low sneak skill will make this quite difficult. Watch out for the guard in the center. In this first area there are many common dwemer artifacts that are directly on display or are in display cases. There are also display cases with expert difficulty locks further into the room that contain weapons, and there are a couple of bookcases with adept difficulty locks with books. One of the Stones of Barenziah is in the room behind the gate to the left as the Dragoborn enters. In this same room is a chest with an expert level lock with valuable items.
 * Head up to Calcelmo's Laboratory, which is restricted; the guards will attack on sight. In the laboratory in an area to the left there is a journal and Spider Control Rod. After a few moments there will be a guard that will walk through the other two doorways opening them up. These guards can be killed with no bounty, a task that can be aided with Aicantar's Spider by using the control rod.
 * The doorway on the left is barred so the right path is the only path available. Find or pickpocket Calcemo's Laboratory Key, or pick the master lock to go into the next area of the laboratory. Two guards will be talking and eventually travel down a hallway.
 * Either follow the guards and sneak by to get to the staircase to the next area, or go the opposite path and get to the stairway. Going the opposite way of the guards will lead to a hallway filled with a gas that is highly lethal and quickly drains health. Opposite the hallway is a button that if stepped on will clear the path, run through before the gas fills the room again. An object (such as the nearby Markarth guard's body) can be left on top of the button to remove the gas. The Argonian Histskin power can completely negate the damage from the gas. Poison resistance does not grant immunity to this damage.
 * Alternatively, there is valve on a column near where the two guards walk. Turning the valve activates a spinning blade trap which can be used to kill the guards, while going completely unnoticed. (It is on the side of a stone pillar facing away from the patrolling guards a little above a lit lantern).
 * The next room has a patrolling guard and Calcemo's nephew Aicantar sitting on a chair in front of a table. At the end of the floor is a valve that can be activated. An explosion will happen that will make Aicantar flee and make it possible to pass and head up to the tower. The explosion can be timed so that the patrolling guard doesn't die. If guards in the previous room are still alive, they will also run through this room.
 * Continue along through the next couple of doorways to the door leading to the wizard's balcony. In the room before the balcony there is a Larceny Target called the Dwemer Puzzle Cube, which may be taken to Delvin Mallory for leveled gold. On another table there is also a chest with valuable loot, plus the enchanting book Twin Secrets.
 * Follow the balcony up and to the right and enter Calcelmo's Tower. Then head up to Calcelmo's Stone. Find a roll of paper and charcoal, which are found in abundance in the room before reaching the stone tablet, before activating the stone. There is also a copy of Chimarvamidium (Heavy Armor skill book) on one of the tables.
 * Once the Dragonborn makes the rubbing, Aicantar, two guards (or three guards without Aicantar) and Captain Aquilius will enter the tower. Aicantar insists that somebody is trying to sabotage his uncle's research, and demands that the guards search the tower from top to bottom.
 * With a high enough Magicka and Illusion, it's possible to neutralize all four hostiles using one or two pacify area spells. After they are neutralized, walk out the door and slide down the waterfall.
 * Alternatively, it is possible to just sneak past the guards and reach the door to the balcony. Continue to retrace your steps back to the room previous to the balcony, then take a right (the door to the room is barred - unbar it). This room will lead to the starting chamber of Calcemo's Laboratory, allowing you to return to the Museum.
 * Killing the guards and Calcelmo's nephew seems to only occasionally incur a bounty.
 * Sneak and jump down to the left after duplicating the stone and hide where the guards stop, when they do their dialogue simply sneak behind their backs and leave room.
 * Once out of the room with Calcelmo's nephew squeeze between the rocks on the left (looking at the tower stairs) and a wall. Follow this down to a nice view of the waterfall and drop into the pool below. The compass will be pointing in the direction of Markarth. Literally the best thing to do is to walk through between the rocks and carry on walking. It's the cleanest way; with no loss of health. You should not jump! Using the Become Ethereal shout will make sure you don't lose any health. Once you have dropped into the pool, the objective marker will automatically update to the Frozen Hearth's cellar in Winterhold.
 * Return to Enthir and Karliah at the Frozen Hearth's cellar in Winterhold.

Rewards

 * Nightingale Blade, from Karliah, previously owned by Gallus Desidenius

Trivia

 * This is one of the few Thieves Guild quests in which it is allowed to kill an enemy to complete it.
 * A way to get Calcelmo's Key to the Museum is to defeat the giant frost spider Nimhe inside the Nchuand-Zel Excavation Site. This method will make the guards in the first section of the Museum neutral.
 * Instead of fighting Nimhe, complete "The Book of Love" quest and Calcelmo will give the key if asked.
 * An aid to sneaking through Calcelmo's Laboratory is to use the various traps in the area. If used properly, all guards can be neutralized without getting a bounty.
 * To avoid almost all confrontations within Calcelmo's Laboratory, repeatedly try to activate near the edge of the barred door to the left of the entrance. If done correctly, with luck, it will remove the bar and open the door allowing access opposite the puzzle cube, with the door to the wizard's balcony just to the left.
 * Enthir becomes a guild fence, if the Dragonborn is not already a member of The College of Winterhold, in which case he is automatically a fence.
 * Once the quest is complete, immediately upon exiting Calcelmo's tower there is a narrow path leading to Markarth’s waterfall. Drop down it to make a quick exit. There are two skeletons and two Septims at the bottom. This also may be referenced by some of the guards saying "Don't trip".
 * Enthir's dialogue after he gets the rubbing has a typo, he says 'undertsand' instead of 'understand'.
 * If you Shout in Calcelmo's Laboratory, with the door near the first valve open, the normal guard will come over to you and tell you not to shout, even if in sneak. After the dialogue he will catch the Dragonborn for trespassing.
 * The journal entry still reads "I'll have to find a way to make the information more portable" even after making the rubbing.
 * Aicantar has an alternate dialogue in the lab about hearing a noise (instead of a saboteur) if you made it past him without activating a trap in the previous room.

Bugs
Трудные ответы