At first glance, these puzzles may seem impossible to solve, especially as no spells seem to affect them, and there doesn’t appear to be any way of inputting an answer directly. Exploring the area further, players may find two switches embedded in the nearby walls, one marked with ?, and the other with ??. These are used to input the correct answers, but short of brute forcing the solution with trial and error, how does one go about figuring them out? The trick, once known, is surprisingly simple and makes solving these once headache-inducing puzzles trivial.
For more Hogwarts Legacy Guides, don’t forget to check out:
- Hogwarts Legacy: How Gear Works
- Hogwarts Legacy: How to Open Locked Doors
- Hogwarts Legacy: How to Unlock the Broom and Other Mounts
How to Open the Arithmancy Doors
What at first appears to be some terribly complex and esoteric puzzle involving numbers and strange beasts, is actually a surprisingly simple Maths problem. Knowing that, many players will correctly assume that each beast represents a different number. And after noting that the beasts always appear in the same order around each door, they may incorrectly assume that their positions correlate to the numbers 1-10.
However, a thorough exploration of the Library Annex (directly above the Divination Class Floo Flame, to be precise) will result in the discovery of a cheat sheet in a chest beside a blackboard and the very first Arithmancy Door. This tells the player that each symbol actually represents the numbers 0-9 (loosely based on the number of horns or limbs seen in the picture). Handily, this sheet depicts each magical beast and the number they represent. For simplicity’s sake, and to save you from having to find it for yourself, see both the picture of the sheet and the list below.
- 0 – Demiguise
- 1 – Unicorn
- 2 – Graphorn
- 3 – Runespoor
- 4 – Fwooper
- 5 – Quintaped
- 6 – Salamander
- 7 – Grindylow
- 8 – Acromantula
- 9 – Hydra
An easy way to remember it is, as each Door is bordered with these symbols in the same order, start at 0 with the creature on the bottom left (the Demiguise) and count up to 9 as you go up and around the door clockwise from symbol to symbol. Armed with this knowledge, all players have to do to open the door is mentally replace the symbols with their corresponding numbers to solve the Maths problem. To do this, the numbers on the three points of a triangle must add up to make the number in its centre.
For example, if the central number is 8 and the two given numbers are 4 and 1, the missing number must be 3, because 4 + 1 + 3 = 8. Therefore, the player will need to roll the ? or ?? on the wall until it shows a Runespoor (the three-headed hydra), as that symbol represents the number 3.
Rotate both the ? and the ?? to the correct beast symbol to make the given totals, and when the player interacts with the Arithmancy door again, it will swing open, allowing them to claim the treasure within. Each puzzle (apart from the very first) will reward players with a brand-new Gear piece and a decorative item for the Room of Requirement.
Found by the Arithmancy Classroom, this cheat sheet tells you the value of each symbol.
Arithmancy Door Locations and Solutions
There are 12 Arithmancy Doors in total, scattered across Hogwarts castle.
Arithmancy Door #1 – Divination Classroom rafters
This is where players will find the Arithmancy cheat sheet in a nearby chest. Simply travel to the Divination Classroom Floo Flame, turn around and head up the staircase and onto the rafters. Head along the rafter walkway and turn right to find the door at the very end.
Solution – ? = Fwooper (4), ?? = Runespoor (3)
Divination Classroom rafters
Arithmancy Door #2 – Arithmancy Classroom
Solving the first puzzle grants access to the Arithmancy Classroom. Go through the door to enter the classroom and the player will find two new Arithmancy Doors to solve. Start with the one on the left.
Solution – ? = Fwooper (4), ?? = Quintaped (5)
Arithmancy Classroom (Left)
Arithmancy Door #3 – Arithmancy Classroom
Within the same room as Door #2, players will find Door #3. This is the one on the right.
Solution – ? = Salamander (6), ?? = Unicorn (1)
Arithmancy Classroom (Right)
Arithmancy Door #4 – Central Hall
Travel to the Potions Classroom Floo Flame, then turn around and enter the Central Hall. The Arithmancy Door should be visible on the opposite wall directly ahead of you.
Solution – ? = Acromantula (8), ?? = Runespoor (3)
Central Hall
Arithmancy Door #5 – Great Hall
Travel to the Great Hall Floo Flame, then head left and around the pillar to enter a small corridor that end ends with the next Arithmancy Door.
Solution – ? = Acromantula (8), ?? = Runespoor (3)
Great Hall
Arithmancy Door #6 – Charms Classroom
Travel to the Charms Classroom Floo Flame, then simply turn around and walk around the corner to the left to find this Arithmancy Door.
Solution – ? = Graphorn (2), ?? = Grindylow (7)
Charms Classroom
Arithmancy Door #7 – Ravenclaw Tower
Travel to the Ravenclaw Tower Floo Flame. This Arithmancy Door is found beside the spiral staircase leading up to the Ravenclaw Common Room.
Solution – ? = Fwooper (4), ?? = Quintaped (5)
Ravenclaw Tower
Arithmancy Door #8 – Grand Staircase
Travel to the Grand Staircase Floo Flame, then head straight down the spiral staircase one level to find this Arithmancy Door set against the wall.
Solution – ? = Salamander (6), ?? = Grindylow (7)
Grand Staircase
Arithmancy Door #9 – Lower Grand Staircase
From Door #8, continue all the way to the bottom of the Grand Staircase. You will see this Arithmancy Door on the wall before heading down the final stairs to the House Hourglasses. Or head up the stairs from the Lower Grand Staircase Floo Flame until you reach the bottom of the Grand Staircase.
Solution – ? = Demiguise (0), ?? = Quintaped (5)
Lower Grand Staircase
Arithmancy Door #10 – North Hall
Level I Alohomora required. Travel to the Transfiguration Classroom Floo Flame, then turn around and walk through the doors behind you and to the left to enter the North Hall. From there, take the stairs up to the top floor to find a Level I locked door. Unlock it, then turn left at the end of old, cobwebby corridor to find the next Arithmancy Door.
Solution – ? = Salamander (6), ?? = Runespoor (3)
North Hall
Arithmancy Door #11 – Long Gallery
Level I Alohomora required. Travel to the Bell Tower Courtyard Floo Flame, then immediately turn left and unlock the Level I locked double doors behind you. Go down the stairs and turn right to see this Arithmancy Door beside a troll encased behind glass.
Solution – ? = Graphorn (2), ?? = Unicorn (1)
Long Gallery
Arithmancy Door #12 – Faculty Tower
Level I Alohomora required. This tower can be unlocked during the quest “The Caretaker’s Lunar Lament”. Travel to the Faculty Tower Floo Flame, then head through the ornate Level I locked door on the right. Head up the stairs and you’ll see this Arithmancy Door on the other side of the landing.
Solution – ? = Demiguise (0), ?? = Hydra (9)
Faculty Tower
Now that you have found all 12 Arithmancy Doors, have fun decorating your Room of Requirement with your new rewards. Or, see if you can put your new Gear to good use in our Hogwarts Legacy: How Gear Works guide. And for more things Hogwarts Legacy, stick with KeenGamer.
