You're standing in a drafty stone corridor of Ravenclaw Tower, staring at a massive circular door frame adorned with carvings of weird beasts. There’s a giant question mark staring back at you. It’s frustrating. You’ve probably tried casting every spell in your arsenal—Confringo, Levioso, even basic casts—only to have the door sit there, stubbornly shut. You aren't alone. Most players spend their first three hours in Hogwarts Legacy feeling like they missed a math class specifically designed for wizards.
The truth is, these Hogwarts Legacy numbered doors aren't actually "puzzles" in the traditional sense. They’re simple addition problems disguised as occult mysteries. Once you realize that the game is just asking you to count to nine, the magic (and the frustration) evaporates. But if you don't know the starting point—specifically that the number line begins at zero—you’ll be rolling those wall triangles for an eternity.
The Arithmancy Cipher Most People Miss
The biggest hurdle is the cipher. Around the arch of every door, there are ten distinct creatures. If you’re looking for a physical "cheat sheet," you can actually find one in the game. It’s tucked away in a chest in the Arithmancy Classroom, which is located in the Library Annex. But honestly? You don't need the paper. You just need to look at the arch from left to right.
Most of us are programmed to start counting at one. In the world of Arithmancy, that’s a mistake. The first beast on the bottom left is a Demiguise-looking thing, and it represents zero. The next one, the Unicorn, is one. This continues all the way around to the multi-headed Hydra on the bottom right, which represents nine.
Breaking Down the Math
Inside the circle on the door, you’ll see a large number in the center. This is your target sum. Surrounding it are three smaller circles: one with a number, one with a beast icon, and one with a question mark. Your job is to make the numbers and beasts add up to that center total.
Let's say the center number is 24. The top circle shows the number 7. The left circle shows a Hydra (which we know is 9).
$7 + 9 = 16$
To get to 24, you need 8. You look at your mental chart (or the door frame) and find the beast in the 8th position—the Spider. You then go to the wall "die" labeled with a single "?" and roll it until the Spider appears. If there's a second triangle with "??" elsewhere nearby, you repeat the process for the second equation on the door. It’s basic arithmetic. Simple, right? Yet, the game doesn't explicitly tell you this for hours, leaving you to feel like a Squib in a room full of Charms masters.
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Where to Find the Most Troublesome Doors
You'll find these puzzles scattered everywhere, from the Grand Staircase to the depths of the Dungeons. Some are out in the open, while others are tucked behind tapestries.
The Grand Staircase is practically littered with them. There’s one near the Ravenclaw Common Room that catches people off guard because the "?? " button is actually on a different floor or tucked around a corner. You have to use Revelio constantly. Seriously, spam that spell. It highlights the interactive dice through walls, which is often the only way to find where the game hid the rolling mechanism.
The Library Annex Secret
The Arithmancy Classroom itself is the jackpot. It houses two doors right next to each other. If you’re trying to gear up early, this is the spot. The rewards behind these doors aren't just cosmetic; you’ll often find gear that significantly boosts your stats in the early game. Plus, there’s a sense of smug satisfaction in clearing out a room that most other students are just walking past with confused looks.
Why the "Zero" Rule Changes Everything
We have to talk about the Demiguise. It looks like a little sloth-man. In any other context, you'd call it "one" because it's the first thing you see. But the developers at Avalanche Software decided to follow true Arithmancy lore, where zero is a fundamental value.
If you treat the Demiguise as 1, every single puzzle you attempt will be off by one. You'll roll the dice, get the "wrong" answer, and the door will spark with red energy. It won't kill you, but it’s a blow to the ego.
Here is the quick-reference list for the beasts:
- Demiguise: 0
- Unicorn: 1
- Graphorn: 2
- Hydra (Three heads): 3
- Fwooper: 4
- Quintaped: 5
- Salamander: 6
- Octopus/Grindylow creature: 7
- Spider: 8
- Hydra (Many heads): 9
Notice the visual cues. The Unicorn has one horn. The Graphorn has two. The Hydra has three. The Spider has eight legs. The game is actually trying to help you if you look closely at the anatomy of the carvings. The only ones that are truly "tricky" are the Demiguise (zero) and the multi-headed beasts at the end of the sequence.
Common Pitfalls and Technical Glitches
Sometimes, you’ll do the math perfectly, roll the right beast, and the door still won't budge. This usually isn't a bug; it's a "user error" involving the two different dice.
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Every door has a "?" equation and a "??" equation. They correspond to two different wall plates. It’s incredibly easy to accidentally roll the Spider on the "??" plate when it was supposed to be for the "?" plate. Always double-check which triangle you are hitting. The single question mark and double question mark are distinct icons.
Visual Accessibility Issues
If you're playing on a smaller screen or a handheld like a Steam Deck or Switch, those carvings can be hard to see. The difference between the 7-headed beast and the 9-headed beast is subtle when the lighting is moody. If you're struggling to identify the carving, use your Lumos spell to brighten the area or look at the number of appendages. The game designers were surprisingly literal with the math-to-body-part ratio.
Beyond the Door: Is the Loot Worth It?
Honestly? Usually. Inside these rooms, you’ll find Collection Chests. These are vital if you're a completionist looking to 100% the game. They contain furniture for your Room of Requirement and high-tier gear appearances.
In the early game, the gear found behind Hogwarts Legacy numbered doors can provide a massive jump in your Defense or Offence stats. By mid-game, you’re mostly doing it for the "Appearance" unlocks so you can stop looking like a mismatch of Victorian leftovers and start looking like a proper wizard.
How to Master Arithmancy Doors Fast
Don't overthink the lore. You don't need to read every scrap of paper in the library to "unlock" the ability to open these. You can open them the second you step foot in the castle.
- Stand in front of the door and interact with it to reveal the numbers.
- Locate the "?" and "??" plates on the nearby walls.
- Count the icons around the door frame starting from 0 (bottom left) to 9 (bottom right).
- Subtract the known values from the center number to find the missing value.
- Roll the plates to the corresponding beast and claim your loot.
If you’re ever in doubt, just remember: the Unicorn is 1, and the Spider is 8. Everything else falls into place around them. If you’ve been stuck on a specific door in the Great Hall, go back there now. You’ll probably solve it in under thirty seconds.
The real challenge in Hogwarts Legacy isn't the math—it's resisting the urge to spend four hours decorating the Room of Requirement once you finally unlock the furniture hidden behind these puzzles.
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Next Steps for Your Journey
Go straight to the Library Annex and find the Arithmancy Classroom. Even if you don't need the cheat sheet anymore, the room contains three puzzles in close proximity. Solving these back-to-back will bake the "start at zero" rule into your brain so you never have to look up a guide again. Once those are open, head to the Astronomy Wing; there are a few doors there that guard some of the better early-game wand handles. Stop casting spells at the wood and just start doing the math.