Harry Potter Professors Logic Puzzle Walkthrough

Known houses of Professors

Slytherin

• Snape
• Umbridge
• Slughorn
• Carrow

Gryffindor

• Dumbledore
• McGonagall
• Moody
• Lupin
• Hagrid

Ravenclaw

• Flitwick
• Quirrell
• Trelawney
• Lockhart

Hufflepuff

• Sprout

Professors included

• Alastor Moody
• Albus Dumbledore
• Amycus Carrow
• Argus Filch
• Armando Dippet
• Aurora Sinistra
• Charity Burbage
• Cuthbert Binns
• Dolores Umbridge
• Filius Flitwick
• Firenze
• Gilderoy Lockhart
• Horace Slughorn
• Irma Pince
• Minerva McGonagall
• Pomona Sprout
• Poppy Pomfrey
• Quirinus Quirrell
• Remus Lupin
• Rolanda Hooch
• Rubeus Hagrid
• Septima Vector
• Severus Snape
• Sybill Trelawney
• Wilhelmina Grubbly-Plank

Walkthrough

1. McGonagall tells us that column 1 is all female. We know that Quirrell, Lockhart, Lupin, Moody and Umbridge make up row A. As Umbridge is the only female then she has to be in A1.
2. Umbridge tells us that McGonagall, Flitwick, Sprout and Snape all share a diagonal. McGonagall is already placed and only has one diagonal long enough; B1-E4. We know from McGonagalls clue that B1 must be female, therefore B1 is Sprout.
3. Sprout tells us that she is adjacent to only one Slytherin. She is already adjacent to Umbridge, who is a Slytherin, so therefore Snape cannot also be adjacent to her. This makes C2 Flitwick, and D3 Snape.
4. Snape tells us Dumbledore is next to McGonagall. Flitwick tells us the headmasters are all adjacent to each other. As Snape and Dumbledore were both headmasters they must be adjacent. The only way for Dumbledore to be next to McGonagall and still adjacent to Snape is if he is in E3.
5. Dumbledore tells us Professor Dippet is above McGonagall, therefore Dippet is in D4. According to Sprout's clue, there is only one person not from Harry's time at school. This is Dippet, so everybody else is from Harry's era.
6. Dippet tells us that three of the corners have a first name beginning with R. As we have already placed A1, we know that this refers to A5, E1 and E5. We have to go back to McGonagall's clue. Using her clue we can place A5. The only DADA teacher whose first name starts with an R is Remus Lupin, therefore he is A5.
7. Lupin tells us that E1 and E5 have the initials R.H. We know that Rolanda Hooch and Rubeus Hagrid are in this puzzle. As there are no other members of staff during Harry's time at Hogwarts with the initials R.H, then we know that they must be in the two remaining corners. Column 1 is all female, so Hooch goes in E1 and Hagrid in E5.
8. Hooch is adjacent to both Divination teachers. Therefore Firenze and Trelawney must be in D1, D2 or E2. As column 2 is all male Trelawney can only go in D1.
9. Trelawney tells us that the non teaching staff are in column 5. There are three spaces left in that column, and we know from previous clues that Filch, Pomfrey and Pince are in the puzzle. This means that they are all in column 5. B5 is adjacent to Lupin, so needs to be male, which means B5 is Filch.
10. Filch tells us that Pince is in C5. He also tells us he shares a diagonal with a Divination teacher. We have already placed Trelawney and he is not on her diagonal, so he shares a diagonal with Firenze. Firenze has to be in D2 or E2, per Hooch's clue. Only E2 is on Filch's diagonal, so this is where Firenze goes. We can also place Pomfrey in the last free space in column 5: D5.
11. Firenze tells us that one of the Carrows is in the quiz. Thanks to Pince's clue, we know that A3 and B4 have first names beginning with A. We also know that A3 has to be a DADA teacher. The only person that is both a DADA teacher and their first name starts with A is Alastor Moody. Moody is in A3.
12. Moody tells us that Lockhart and Binns are in either A2 and B2, or A4 and B4. B4 has to have a first name starting with A, and as Cuthbert Binns does not, then Lockhart is A2 and Binns B2. This also only leaves A4 in the DADA column, so this has to be Quirrell as he is the only DADA teacher left from Harry's first five years.
13. Thanks to Binns' clue we know there are only two males left to place, and we know that these are Amycus Carrow and Horace Slughorn. We know that B4 has to be one of them, and that they have to have a first name starting with A, so that is Amycus Carrow. This also means that Slughorn must take the last place in the all-male column 2. Slughorn is D2.
14. Slughorn tells us that there is another COMC teacher in the quiz, and they share a diagonal with Hagrid. The only other COMC during Harry's time was Grubbly-Plank. The only space in Hagrid's diagonal is C3, so this is Grubbly-Plank.
15. Grubbly-Plank tells us that C1 is a Muggle Studies teacher. The only two Muggle Studies teachers we know of are Charity Burbage and Alecto Carrow. We know that Alecto Carrow is not in this puzzle thanks to Firenze, so C1 is Burbage. 
16. We know that the Astronomy teacher is in the row C. The only remaining space is C4 and the only Astronomy professor we know is Sinistra, so she is C4.
17. We know the last space belongs to the Arithmancy professor, therefore Vector is B3.