1. Harry’s clue tells us that Molly’s youngest is in A2.  Ginny Weasley must go in A2, since she is Molly’s youngest child.
2. Ginny tells us that her LIVING brothers make up the fourth row.  Fred Weasley is deceased, so we must leave him out.  That means row 4 is as follows:  A- Bill, B- Charlie, C-Percy, D-George, E- Ron.
3. Percy’s clue explains that the two werewolves inhabit the right hand corners, E1 and E5.  That means Lupin and Greyback take up those two squares.  We find out from Ron that the person who maimed his oldest brother (Bill) is adjacent to me.  Fenrir Greyback maimed Bill, and since he can only go in a right hand corner AND be adjacent to Ron, he must be in E5.
4. The only other werewolf then must go in E1.  Lupin is in E1.
5. George’s clue tells us that Rita Skeeter belongs in C2.
6. Fenrir’s clue says that Draco has his cronies directly above and below him.  That means we need three consecutive vertical spaces.  There are only two of those available at this point in the quiz, B1-B3 and D1-D3.  We can, however, eliminate D1-D3 because Lupin (E1) tells us that he is adjacent to two of his friends.  There are only 3 spaces adjacent to him.  Two of those spaces are D1 and D2.  Since he is adjacent to TWO friends, one friend has to take up either D1 or D2, which makes it impossible for Draco and his two cronies to inhabit those spaces.  Since Draco is in the center, he must go in B2.
7. Draco then tells us that Crabbe goes on top, putting Crabbe in B1 and Goyle in B3.
8. Draco also tells us that Dobby is in that column.  The only space left, B5, is where Dobby belongs.
9. Crabbe’s clue says that the only other living being made into a horcrux is adjacent to Ginny.  Harry and Nagini were the only living beings made into Horcruxes.  Harry already exists in the quiz. There is only one space adjacent to Ginny left, so we know Nagini belongs in A3.
10. Nagini explains that the rodent member of the marauders (Wormtail akaPeter Pettigrew aka Scabbers) is right above his most recent owner.  Ron Weasley owned Wormtail in his Scabbers form, so Peter Pettigrew belongs in E3.
11. Goyle’s clue tells us that the last corner, A5, is inhabited by a male half giant.  Hagrid belongs in A5.
12. Back to Rita Skeeter’s clue.  We know Sirius is not adjacent to his old friend the traitor, which is Wormtail.  He cannot be in D2, D3, or E2.  We know Lupin is adjacent to his two non-traitor best buds, James and Sirius.  Sirius must be in D1, D2, or E2.  Since he CAN’T be in D2 or E2, the only place left for him is D1.
13. Sirius tells us that his column, column D, contains only Gryffindors.  Hagrid’s clue says that Dumbledore is in the last space in his house’s column.  Dumbledore was a Gryffindor, so he must go in D5.
14. Dumbledore tells us that his deputy headmistress, McGonagall, is adjacent to Lockhart’s successor (Lupin).  The only spaces left that are adjacent to him are D2 and E2.  We know from Pettigrew’s clue that she is NOT in her house’s column (column D, since she’s a Gryffindor), ruling out space D2.  McGonagall goes in space E2.
15. McGonagall tells us the last animagus is to her left.  There are only 5 known animagi that live during the series.  The last is James Potter.  he goes in D2.
16. James’s clue informs us that Bellatrix is not adjacent to anyone she killed.  That rules out space C1, because it is adjacent to Sirius.  She also killed Dobby, who is adjacent to C5, so no C5.  She cannot go in column D, since she was not a Gryffindor, so space C3 is the only space Bellatrix fits.
17. This leaves D3 as the final space in row 3, and we know Hermione belongs in row three thanks to Dobby.  She was a Gryffindor, so D3 it is.
18. Bellatrix tells us that the boy whose parents she tortured (Neville Longbottom) is adjacent to the only wizard her master ever feared.  Voldemort feared Dumbledore, so Neville must go in the only space left adjacent to him, C5.
19. The last space is Voldemort.  The purpose of the quiz was to find him, after all!