Lord Voldemort's Request
Chapter 20 of Harry Potter and the Half-Blood Prince: Lord Voldemort's Request
Harry and Ron are discharged from the Hospital Wing together. Meeting up with Hermione, they head to breakfast, passing a small girl studying a tapestry. Startled, the girl drops the scales she had been holding; Hermione repairs them for her, and then mentions that Ginny and Dean had an argument. Harry tries to react calmly to this news, but Hermione remains suspicious that he harbors feelings for Ginny.
Continuing on, the Trio runs into Lavender, who is miffed she was not told Ron was being discharged, and also that Hermione is with him. Harry and Hermione walk off, and Ron arrives at breakfast a half hour later; he is upset and not talking to Lavender. Hermione seems secretly pleased by this development.
Later that evening, Harry arrives for his appointment with Professor Dumbledore. He is embroiled in a discussion with Professor Trelawney, who is upset that Firenze is still teaching Divination. After she leaves, Dumbledore gently chastises Harry for failing to retrieve Professor Slughorn's memory. Without it there is little point in continuing their lessons. Dumbledore and Harry then review what they have learned thus far: Voldemort killed his father, framed his uncle, Morfin, and took the Peverell ring; after returning to Hogwarts he asked Slughorn about Horcruxes.
Now they enter the realm of deep speculation. At this session, there are only two memories. The first belongs to Hokey, a House-elf who worked for an elderly rich woman. At that time, Tom Riddle was working as a buyer for Borgin & Burkes. Tom's career choice surprised many, as it was assumed he was headed for a political career and as the Minister for Magic. But Tom had first approached Armando Dippet, the Headmaster then, for a teaching post at Hogwarts. Dippet declined him, saying he lacked experience.
In Hokey's memory, Tom Riddle visits Hepzibah Smith, who claims to be Helga Hufflepuff's descendant. Hepzibah shows Riddle two coveted family treasures. One, a cup once belonging to Helga Hufflepuff that was bought from Borgin & Burke's. The other is a locket once owned by Salazar Slytherin. The locket was sold to Hepzibah by Borgin & Burke's, who bought it off some poor woman. Harry recognizes the locket as the one seen earlier in Merope Gaunt's possession, and Riddle clearly also recognizes it.
Two days later, Hepzibah died, and her treasures went missing; Hokey confessed that she had mistakenly poisoned her. Riddle considered the locket was rightfully his, and Dumbledore suggests that he also stole the cup because of his deep attachment to Hogwarts; why he wanted it must wait for another lesson.
The second memory is Dumbledore's as Hogwarts Headmaster meeting with Riddle. Ten years after Hepzibah Smith's death, Riddle has again applied to be the Defence Against the Dark Arts teacher. His facial features have changed somewhat; while unlike the snake-like mask that Harry remembers, this is certainly not the handsome Tom Riddle seen in the previous memory. Dumbledore confronts him about his true motives for wanting the position and his rumored behavior. He turns down Riddle for the job, saying he knows Riddle has a new name (Voldemort) and that his Death Eaters are in Hogsmeade.
Returning to the office, Dumbledore tells Harry that ever since he refused Voldemort's request, there has never been a Defence Against The Dark Arts teacher who lasted more than one year.
There is now a possible explanation for Defence Against the Dark Arts teachers having such short tenures: Dumbledore believes that Voldemort cursed the position after he was rejected for it. Dumbledore must either have been hoping that the curse would be broken when he appointed Professor Snape as the new Defence Against the Dark Arts teacher, or otherwise never expected him to last any longer than his predecessors. Dumbledore trusts Snape, though it is still unclear why; at least two of the previous five incumbents have been driven mad: (Professor Lockhart by a self-inflicted backfiring charm, and Professor Umbridge by the Centaurs). One, (Professor Quirrell), has died, and another (the false Professor Moody) had his soul sucked out by a Dementor. Only Professor Lupin left the post relatively unscathed, at least physically. Thus, the post does have a definite risky element to it, leaving us wondering why Dumbledore would appoint such a valued teacher and someone he deeply trusts in a position where harm could easily befall him.
As Dumbledore implies, the memories seen tonight do not significantly increase our understanding about Voldemort. Dumbledore clearly believes that the missing memory contains vital information for Harry to understand Voldemort's plans.
Also, in the previous chapter, Draco was seen accompanied by two girls, both looking sulky and rebellious. Now there is a small girl standing in the seventh-floor corridor studying a tapestry; we also saw a small girl standing in the seventh-floor corridor earlier. Each time the girls drop something, presumably from being startled.
The tenor of Lavender and Ron's encounter is another clear indication that their relationship is on the rocks. Whether they can patch up their differences and go on is unknown, but we suspect not. Ron seems to have little inclination (or ability) to deal with the issues, instead avoiding them, in this case, by feigning sleep.
- Why did Ginny argue with Dean? What is Harry's reaction to the news? Why is Hermione suspicious of this?
- What do the two memories reveal about Voldemort?
- Why does Dumbledore tell Harry there will be no more lessons? What does Harry need to do?
- What is significant about the seventh floor?
- Why would Tom Riddle have taken such a lowly job at Borgin & Burke's?
Further Study 
- What reasons might Dumbledore have had to refuse Tom Riddle the Defense Against the Dark Arts position? What's the long-term result of this decision?
- Why does Harry continually see one or two young girls loitering in the halls?
Greater Picture 
Aberforth is Dumbledore's brother, and according to an interview with the author and information in the seventh book, the bartender of the Hog's Head. It is safe to assume he has been so for some time, and likely was at the time that Voldemort approached Professor Dumbledore for a job. That is most likely the reason Dumbledore knows there are Death Eaters in Hogsmeade.
There is some speculation, both within the book and by fans, about Voldemort's true purpose in visiting Hogwarts to apply for the Defense Against the Dark Arts position. Dumbledore states that Voldemort probably wanted a teaching position there so he could investigate Hogwarts and all its secrets with impunity. There would also be many impressionable young minds to recruit to his peculiar beliefs. Dumbledore also apparently suspected that Voldemort was attempting to make a Horcrux – possibly using Godric Gryffindor's sword. Some fans suggest that he was planting a Horcrux there (which proves to be true in Harry Potter and the Deathly Hallows). That would fit his "style" — hiding a Horcrux under Dumbledore's nose, basically saying that he knew Dumbledore's school better than Dumbledore himself did. Voldemort may have partially used the interview as a ruse so he could hide Rowena Ravenclaw's Diadem, one of his Horcruxes, inside Hogwarts. His intent here was actually to keep the Diadem safe, convinced he was the only living person who knew about the Room of Requirement.
Voldemort probably told Draco how to summon the Room of Requirement. Putting the clues together, as Harry does in the next chapter, we will see that Draco is working on his project in this room. Crabbe and Goyle, disguised as little girls by stolen Polyjuice Potion, stand guard outside, dropping objects when it is unsafe to exit the room. Although Draco would already have known about the Room of Requirement after Dumbledore's Army was discovered there the previous year (in Harry Potter and the Order of the Phoenix), it seems Voldemort will continue to be under the assumption throughout the next book that he and Draco are the only ones who know it exists. Clearly Draco failed to mention to the Dark Lord that he already knew the Room of Requirement existed; one might wonder what other information Draco is keeping from Voldemort. Presumably, despite working in the room where it is hidden, Draco knows nothing about the Diadem Horcrux.
In the summer preceding this school year, Dumbledore learned he had approximately one year left to live after he was inflicted with a fatal curse. He specifically required Snape to kill him by the school year's end, thus protecting Draco Malfoy from executing Voldemort's assassination plot. Realizing he will only last out the year, and that Snape will be accused of murdering him, Dumbledore knows that Snape's tenure as Defence Against the Dark Arts teacher would be limited in any case. This is likely why Dumbledore repeatedly refused Snape the post: Snape is too talented a teacher, too valuable an ally, to risk losing. After this year, it will no longer matter, so placing him in the cursed post will do no harm. More importantly, it aids Dumbledore's plan to retrieve Slughorn's true memory by bringing him back to Hogwarts to fill Snape's vacated potions position.
The ongoing byplay with an increasingly alcoholic Sybill Trelawney is actually aimed at two related revelations. First, Harry discovers that Trelawney has been hiding her sherry supply in the Room of Requirement, and that she heard Draco celebrating his success. As Trelawney accompanies Harry to Dumbledore's office to report this, she reveals that it was Snape who carried the prophecy's first half to Voldemort, which in turn resulted in James and Lily Potters' deaths.