Arithmancy Door Checklist ♦ Hogwarts Legacy

Every Arithmancy door blocks the path to one collection chest and one average gear/coin chest. The doors show two relationships with unknowns labeled “?” and “??”. The equations are solved by taking the sum of the triangle’s corners to equal the center. Choose the creature that solves the equation and enter it on the roll blocks. In some cases, the roll blocks are placed at a significant distance or up or down a floor from the door. More details on the solutions and the creatures used are provided below.

1. Central Hall Southeast – down the southern stairs from the heart of Central Hall in the southeast corner. The “??” roll is up a couple of flights of stairs overhead.
graphorn (2) + 11 + ? = 21 … acromantula (8)
quintaped (5) + hydra (9) + ?? = 17 … runespoor (3)

2. Great Staircase Great Hall Upper Landing – down the upper path from the Great Hall to the Great Staircase beyond the Hogwarts Architect with a sharp left about-face before the staircase. The “?” roller is on the level below, backtracking to the architect and down some stairs to the right.
graphorn (2) + 4 + ? = 6 … demiguise (0)
5 + 1 + ?? = 11 … quintaped (5)

3. Great Staircase Arithmancy Door Landing – set in the outer wall of the Great Staircase between the tower staircase to the Trophy Room and the Ravenclaw Tower hallway landing. The “?” roller is up the left stairs while “??” is facing the door on the center column.
graphorn (2) + 15 + ? = 23 … salamander (6)
runespoor (3) + hydra (9) + ?? = 19 … grindylow (7)

4. Arithmancy Classroom – on the spiral stairs up to the Divination Classroom, an opening to the right enters an attic space. Halfway down the catwalk, here on a spur to the right, is the Arithmancy Classroom entrance.
runespoor (3) + 2 + ? = 9 … fwooper (4)
0 + 1 + ?? = 4 … runespoor (3)

5. Arithmancy Classroom Closet – inside the classroom, the right door leads to a small siding room.
quintaped (5) + 6 + ? = 17 … salamander (6)
grindylow (7) + 0 + ?? = 8 … unicorn (1)

6. Arithmancy Classroom Office – the left door in the classroom is set with an office desk and its own privacy.
salamander (6) + quintaped (5) + ? = 15 … fwooper (4)
13 + demiguise (0) + ?? = 18 … quintaped (5)

7. Charms Lounge – opposite the lounge in the Astronomy Tower near the Charms Classroom, this door leads to the thestral decorated closet.
0 + 3 + ? = 5 … graphorn (2)
unicorn (1) + 4 + ?? = 12 … grindylow (7)

8. Ravenclaw Tower – between the hallway to the Great Staircase and the spiral stairs to the Ravenclaw Commons, this dark paneled room contains another door. Both rollers are in the room, but far from the door.
acromantula (8) + 1 + ? = 13 … fwooper (4)
13 + runespoor (3) + ?? = 21 … quintaped (5)

9. Great Hall – each of the rear corners of the hall contains a hallway. Facing the exit doors, the left path leads up some stairs to a house cabinet and a storage vestibule, while the right ends at this door.
7 + hydra (9) + ? = 24 … acromantula (8)
11 + demiguise (0) + ?? = 14 … runespoor (3)

10. Faculty Tower – on the first landing up from the base floor of the Faculty Tower, beyond the level 1 locked door that Gladwin Moon teaches you Alohomora to break first.
5 + acromatula (8) + ? = 13 => 0 … demiguise (0)
3 + graphorn (2) + ?? = 14 => 9 … hydra (9)

11. Bell Tower end of the Long Gallery – through the Bell Tower’s east-facing level 1 lock door, down the stairs, and to the right before entering the Long Gallery. This closet contains many statuary pieces and the Gorgon Portrait.
12 + acromantula (8) + ? = 22 => 2 … graphorn (2)
grindylow (7) + unicorn (1) + ?? = 9 => 1 … unicorn (1)

12. Bell Tower Wing History of Magic Tower Room – through the northeast door from the Bell Tower Hall toward the History of Magic Classroom and take the left before the class door. Continue left up the stairs. Pass through the level 1 lock door and make for the back of the room to this door.
graphorn (2) + 2 + ? = 10 => 6 … salamander (6)
3 + 1 + ?? = 7 => 3 .. runespoor (3)

The Arithmancy doors tie basic Arithmancy to magical Beasts lore. Every puzzle is a sum, A + B + C = D, where A, B, and C are the corners of an equilateral triangle and D, the sum, is at the triangle’s center. Then there are the beasts. The cube chest outside the Arithmancy classroom, near the Divination Classroom’s stairs, contains a lore document listing the creatures and their numerical values. This confirms the position on the doorframes, clockwise, left to right, 0 through 9. The images shown are as follows:

0. demiguise
1. unicorn, one horn
2. graphorn two horns
3. runespoor, three heads
4. fwooper, wings + legs
5. quintaped, five legs (I have no confirmation for this name; I have seen it in a few other sources.)
6. salamander, head, tail, four limbs
7. grindylow, seven tentacle limbs or six and a head?
8. acromantula, eight legs
9. hydra, nine heads in this case

Also outside the Arithmancy Classroom is a poorly erased chalkboard bearing the solution to the sum. Spin each six-sided wall tumbler die “?” and “??” to set the beast whose value solves the equation. The single or odd mark “?” is the odd-numbered beast, while the even or pair of marks “??” is the even-numbered beast.