Before the final exam
Days passed.
Every day a new academy is conducting an examination and Sam is attending them all. Along with him at least one other member from Dusk who is in Divine Plane is attending the examination. Sam is quitting but one member from Dusk is accepting the test.
While this process is going on many people started hating and resenting Sam.
They tried to stop him from attending some exams, but they couldn't get a hold of him. Even the people who sneaked into the inn disappeared without a trace. Some even speculated that Sam already belonged to some other academy and he is just trying to piss off the rest to dishonor them.
In a way their speculation is right.
But Sam has way more planned than just some dishonor.
While Sam is doing all of this, something else is going on in his mind. He is sure that the Demi-gods he came across in the tasks belong to these Olympus academies. So, they should at least have a fleeting knowledge of who Sam was.