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On your way through Hogwarts you probably came across some Arithmancy doors. Here’s a very simple guide to finding and solving them!
The numbers… what do they mean?
It’s very easy! They go from 0 to 9 starting from the left side. 
When you interact with the door it shows you two simple math problems: 
Somewhere close are two blocks in the wall. You can interact with them to “roll” different pictures. The ? block corresponds to the upper one, the ?? block to the lower one. You can also see this when looking at the alignment of the triangles.
The numbers on the corners of the triangles need to add up to the numbers in the middle.
There’s no sound cue for the right solution, so once you are done just go back to the door and open it.
Locations
Named after the nearest Floo point.
Greem Circle: Floo Point
Yellow/Orange Circle: ? and ?? blocks
Astronomy Wing
1. Charms Classroom
2. Transfiguration Classroom
Still locked for me, coming soon!
The Grand Staircase
1. Grand Staircase
The ?? block is directly next to the Floo point, the door and the ? block are up the stairs
2. Grand Staircase
Go up the Spiral staircase until you reach the door. ?? is right across from the door on the middle column.
3. Ravenclaw Common Room
The Great Hall
1. Great Hall
Library Annex
1. Divination Classrom
2. & 3. Divination Classrom
After heading through door six and following the corridor you get to the Arithmancy classroom, which has two doors in it.
4. Potions Classroom
5. Potions Classroom
Locked behind Door, coming soon
South Wing
1. Faculty Tower
Still locked for me, coming soon!