To solve an Arithmancy door in Hogwarts Legacy, treat each triangle as an addition equation. Convert the creature symbols to their fixed values from 0 to 9, subtract the two known values from the triangle’s center number, and set the nearby question-mark dial to the creature representing the remainder. Solve both triangles, then interact with the door.
How the Hogwarts Legacy number doors work
Each Arithmancy door has two triangular equations. The large number in the center of each triangle is the required total. The three outer entries—numbers or creature symbols—must add up to that total.
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Two entries are visible in each triangle, while the third is represented by a question mark. Your task is to calculate that missing value and select the matching creature on a nearby dial.
What the animal symbols mean
Every creature drawing has one fixed value from 0 through 9; it is not decorative. The symbols appear in a set order around the door arch, forming the cipher used by every Arithmancy door.
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Use the arch as the cipher
- Find the symbol sequence around the door frame.
- Identify the zero-valued symbol at the start of the sequence.
- Count forward through the symbols to assign values 0, 1, 2, and so on up to 9.
The in-game Arithmancy Study Guide note records the same mapping. Once you have identified the sequence, it applies to the other Arithmancy doors throughout Hogwarts.
Step-by-step solution
- Inspect both triangles. Record the center total and the two visible entries in the upper triangle, then do the same for the lower triangle.
- Convert creatures into numbers. Use the arch sequence or the Study Guide note to translate each visible creature.
- Calculate the missing value. Use
missing value = center total − known value 1 − known value 2. - Locate the matching dial. The question-mark dials are normally mounted on the wall close to the door, so check the immediate area if one is not obvious.
- Set the first dial. Cycle it until it displays the creature assigned to the missing value for the upper triangle.
- Set the second dial. Repeat the calculation for the lower triangle and select its matching creature.
- Interact with the door. Both dials must be correct before the door will open.
Worked example
Suppose a triangle’s center number is 17. One visible entry is 6 and the creature in the other visible position is worth 4:
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17 − 6 − 4 = 7
The missing entry is therefore 7. Find the creature assigned to 7 in the arch sequence and set that triangle’s question-mark dial to it. This calculation is a generic example rather than the answer to a particular door.
Where to find the first clue
The first explanatory note is on the Library Annex route near the Divination Classroom and Arithmancy Classroom. Finding it gives you the complete 0–9 symbol mapping. You can then solve later doors by reading the arch sequence and applying the same arithmetic.
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Choosing a solving method
| Approach | Best for | Trade-off |
|---|---|---|
| Study Guide note | Players who want the cipher stated explicitly | Requires finding the note first |
| Count the arch symbols | A spoiler-free solution at any door | You must identify the zero symbol and count carefully |
| Manual calculation | Players who want to solve each puzzle themselves | Requires translating symbols and doing both subtractions |
| Location-and-solution list | Players who only want to open doors quickly | Reveals puzzle answers and reduces discovery |
Troubleshooting a door that will not open
One dial is wrong
Recalculate both triangles independently. A single incorrect dial prevents the interaction from succeeding, even if the other triangle is correct.
You cannot identify a creature’s number
Do not guess from the drawing. Return to the arch sequence, locate the zero-valued symbol, and count forward to the creature in question. The Study Guide note provides the same reference.
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- EXPLORE AN OPEN WORLD. The wizarding world awaits you. Freely roam Hogwarts, Hogsmeade, the Forbidden Forest, and the surrounding Overland area.
- BE THE WITCH OR WIZARD YOU WANT TO BE. Learn spells, brew potions, grow plants, and tend to magical beasts along your journey. Get sorted into your house, forge relationships, and master skills to become the witch or wizard you want to be.
- EXPERIENCE A NEW WIZARDING WORLD ADVENTURE. Experience the wizarding world in an unexplored era to uncover a hidden truth from its past. Battle against trolls, Dark Wizards, goblins, and more as you face a dangerous villain threatening the fate of the wizarding world.
You cannot find the question-mark dials
Search the wall and nearby surfaces around the door. The dials are usually close to the entrance rather than in a separate room.
The arithmetic produces an unexpected value
Check that you converted both visible creatures before subtracting and that you copied the center number correctly. Each missing value should correspond to one of the ten symbols, from 0 through 9.
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What Arithmancy doors contain
Arithmancy doors are documented in the Library Annex and around the Arithmancy Classroom area, with additional examples elsewhere in Hogwarts. Opening them leads to hidden rooms or chests and associated loot. The contents are not established as one fixed reward table for every door, so treat each opening as a separate exploration reward rather than expecting an identical item.
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