Upon examination the door leading to Suidacra's office is significantly different from the others in the hall way, it bears no handle, or panel with which one could pull or push. The other doors have hinges on the right side, allowing them to swing outwards if opened, but the professor's door doesn't have hinges on either side, more over there doesn't even seem to be a crevice between the stone of the wall and the wood of the door.

Cendrion's further examination of other doors indicates that each use 3 rotary dials of numbers 1-6 as a means to unlock and open, but the dials on this door are held in place by faint glowing lines preventing other combinations from being selected.

Siobhan recognizes this as an arcane lock, a layer of magical enchantment applied to a physical one.

As Cendrion concludes his examination, his eye alights upon a oddly shaded piece of slate embedded in the floor.

Spoiler: Beneath the slate
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Beneath the piece of slate - a folded bit of parchment with an identical painted wax seal.

My friends you've all but finished, however, many a task is left incomplete upon its zenith,

To remove the magical protective elements, the word "open" must be spoken by four tongues in four different tongues at the same time, as for the dial,

The first number is equal to how many passengers the carriage delivered tonight.
The second number is less than the first but 2 more than the third.
The third number is not 1.

As with all good things in life, you have but a single chance, take your time and think, but not too long,
I have tea, hot stew and fresh fruit waiting.

Professor Suidacra