Dr. Boris Balinkoff is a eccentric crazy scientist who lives in a castle on an island somewhere near the Castaways. His only companions are his manservant, Igor, and his pet parrot, Timothy.
Balinkoff has twice tried to involve the castaways in his crazy schemes and experiments. Lured by a signal fire, he originally appeared pretending to be a rescuer, but he eventually reveals to Mr. Howell that he has discovered a way to put the mind of one animal into the body of another one with an invention. Ready to try it on human subjects, he switches the minds of the Castaways, Mr. Howell with Gilligan, Mrs. Howell with the Skipper, Mary Ann with the Professor and possibly Ginger with his assistant Igor, although he seems unaware of this last transference. Eventually, everyone gets their own personality back, and Balinkoff is made a victim of his own device, exchanging his mind with a cat as Igor exchanges minds with a dog.
Inexplicably, Balinkoff somehow returns to the island with Igor and tries to hypnotize the castaways into becoming robots using mind control rings so he can rob Fort Knox. Unfortunately, the Castaways in their robotic state manage to drive him away with coconuts and smash his remote control by chance, driving him away while somehow not recognizing him from the earlier encounter.
- Dr. Balinkoff was played by actor Vito Scotti, who also guest starred as a Japanese Sailor, who lands on the Island and doesn't realize that World War II is over in So Sorry, My Island Now. He reprised the role in fantasy segments in Diogenes, Won't You Please Go Home?. He makes the most appearances in the series over Hans Coreid (2), Eddie Little Sky (3), Russ Grieve (3), Denny Scott Miller (2) and George A. Neise (2).
- In the first episode, the castaways are shown escaping in Dr. Balinkoff's boat back to the Island, where it promptly sinks and strands them again. His second boat must be a back-up or a spare.
- Goofs - Balinkoff is puzzled to find out Igor changed places with Ginger; yet, he was the only one who could have operated the machine while his two subjects are imprisoned in the machine.
- It is also unrevealed as to how Balinkoff (cat), Igor (dog), the cat (Balinkoff) and the dog (Igor) escape from the machine when the lock is on the outside. While its possible the locking mechanism had an interior switch that could be disabled from the exterior, it is unclear how the dog and cat as Igor and Balinkoff knew how to activate it.
- Without knowing how the device works, it is unclear how the device cleanly transfers two minds at once with mixing up the memories, combining them or just overloading.
- In Ring Around Gilligan, Balingkoff also mentions a gamma laser invention which can supposedly immobilize weapons.
- It's not sure why the Castaways fail to recognize Balinkoff unless it took so long to overcome the ring's controls for them to recognize him.
- It is never revealed if the Castaways find Balinkoff's abandoned device in the cave.