Algorithm for finding study groups

[traitboundnotsatisfied]

@residualentropy is responsible for this. Integrates with #4.

Create a backtracking-based algorithm to generate study groups. Just need to make sure this isn't too painfully slow.

Might also want to add a loading screen if necessary. That's fine but a separate issue should be created for it.

[traitboundnotsatisfied]

DO it recursively :)

[TetraTsunami]

Implemented but I don't think we have the API paths yet