One of the first door puzzles you'll likely encounter in Hogwarts Legacy is in the Central Hall of the Library Annex of the school. At the end of the Welcome to Hogwarts quest, you'll need to use a Floo Flame for the first time. You can also do some exploration, puzzle solving, and chest looting first.
How to Solve the Hogwarts Legacy Bridge Fire Problem
In Hogwarts Legacy, how do you open the Central Hall puzzle door?
After speaking to Professor Weasley and Professor Fig in the Central Hall, ascend the stairs to the south and turn left. You'll find a locked door surrounded by an archway marked with various creatures. Examine the door itself, and you'll notice two triangles with creature symbols, numbers, and question marks.
The three numbers on the points on the top of the triangle must add up to the number in the middle of the triangle, which is the spider. So, roll the triangle next to the door until it shows a spider.
The bottom triangle must be 5 + 9 + 17 = the missing creature, which is the hydra. Now, go upstairs and roll the triangle directly above the locked door until it shows a hydra. When you come back down, it should open, and you may unlock two chests, one of which contains the Magical Paintings Conjuration exploration collectible.