The Great Hall is one of the six areas in Hogwarts School of Witchcraft and Wizardry, and it has three Floo Flames: one at the boathouse on the lake, one in the Great Hall itself, and one in the Viaduct Courtyard. One of the school's arithmancy doors is also the location of an ancient magical art of arithmancy, which must be solved with a little help.
Related: Hogwarts Legacy's Demiguise Statue locations
In Hogwarts Legacy, how do I open the puzzle door in the Great Hall?
The Great Hall puzzle door is at the end of a corridor leading off the northeast corner of the Great Hall itself. Head east from the Great Hall Floo Flame, then turn left. The “?” and “??” triangles are also located in this same corridor.
The demiguide is 0 and the snakes are 9; the “?” is represented by the spider icon.
The bottom triangle reads 11 + demiguise (0) +?? = 14. This means that the "??" must be 3, which is represented by the hydra, so roll the "??" triangle until it displays a hydra. Now you may open the door and loot the chests inside, one of which contains the Crests Conjuration exploration collectible.