Word for random knowledged person

Solution 1:

1. sage

Ken Jennings is a very sage man. He won 74 editions of the Jeopardy! Game Show.

One of the meanings from dictionary.com:

wise, judicious, or prudent

2. savvy

Ken Jennings is a very savvy man. He won 74 editions of the Jeopardy! Game Show.

One of the meanings from dictionary.com:

experienced, knowledgeable, and well-informed; shrewd

3. astute

Ken Jennings is a very astute man. He won 74 editions of the Jeopardy! Game Show.

One of the meanings from dictionary.com:

clever; cunning; ingenious; shrewd

4. adroit

Ken Jennings is a very adroit man. He won 74 editions of the Jeopardy! Game Show.

One of the meanings from dictionary.com:

cleverly skillful, resourceful, or ingenious

As already listed, eclectic and erudite would also work very well.

Solution 2:

erudite

characterized by great knowledge; learned or scholarly

from dictionary.com