Dumbledore says that Ron is in C2.
Dumbledore says that the four Triwizard champions are in corners. So according to Ron, Fleur must be in A5.
Fleur tells you that Column E has no Gryffindor. This means, according to Dumbledore, that Harry Potter is in A1.
You know from Dumbledore that E5 is a Triwizard champion. According to Fleur, E5 died, so E5 must be Cedric Diggory.
Dumbledore now tells you that the remaining Triwizard champion, Viktor Krum, goes in E1.
Viktor Krum tells you that Igor Karkaroff is in D5.
Harry’s wife is Ginny Weasley. She did not die and she is a Gryffindor. This means she cannot be in Column E, according to Ron/Fleur and cannot be in Row 5, according to Fleur. So if she’s adjacent to Cedric, as Harry says, she must be in D4.
Ginny says that Fred and George are adjacent to her. E3 and E4 are not Gryffindors, according to Fleur. According to Harry and Cedric, James Potter must be adjacent to both Ginny and Dumbledore, meaning either D3 or C4. So the only two places for Fred and George are D3/C4 and C5. Fleur tells you that C5 died, so C5 must be Fred.
George was either D3 or C4. Now you know from Fred that George is D3.
According to George, Lord Voldemort must go in B5.
James Potter has to be adjacent to Ginny (Harry) and has to be adjacent to Dumbledore (Cedric), so James goes in C4.
James Potter tells you everyone who is adjacent to Harry. Two of them are female, and Ron says B1 cannot be female, so B1 must be Vernon Dursley.
Vernon tells you that Petunia is not adjacent to Dumbledore. James tells you she is adjacent to Harry. So Petunia is in A2, meaning Hermione is in B2.
Cedric tells you that Dumbledore is adjacent to all four Marauders. At the moment he is adjacent to only one and only three unknown cells. This means that B3, B4, and D2 are the remaining Marauders. Therefore, according to D3, Neville Longbottom is in A3.
Cedric tells you that Dumbledore is adjacent to all four Marauders, meaning Sirius is B3, B4, or D2. So according to Hermione, Sirius must be in D2.
Fred Weasley tells you that the only Weasley siblings are Percy, Fred, George, Ron, and Ginny. So according to Neville and the fact that B3 and B4 are Marauders, Percy is in A4.
Percy tells you that D1 and E2 are Ravenclaws. This means, according to Sirius, that Severus Snape is either C1 or E3. Lord Voldemort says that Snape and Draco Malfoy are adjacent to each other. Draco is also not a Ravenclaw, so Snape cannot go in C1; he must go in E3 so that Draco can be adjacent to him in E4.
Draco tells you that Roger Davies must go in E2.
Roger Davies tells you that Peter Pettigrew must be in B4.
According to Cedric, B3 must be Remus Lupin.
Lupin tells you that Lucius Malfoy is adjacent to a Muggle. D1 is a Ravenclaw, so not Lucius, meaning Lucius must be in C1.
Snape told you that there is another head of house in the puzzle. The last remaining cell is D1, which Percy says is a Ravenclaw. So D1 must be Filius Flitwick.