Did the professor invent these things on Gilligan's Island?

Ah yes, the professor: the man who famously could create just about anything out of coconuts, palm fronds, and sea shells — but couldn't seem to fix the hole in the boat.

During the castaways' stay on the island, the professor came up with dozens of inventions to make their lives easier (or to serve as a convenient plot device for that week's adventure.) Can you remember if he actually made these gadgets, gizmos, and appliances?