SOLUTION:
Barney won with 100 points, followed by
Otis with 75 points,
Bee with 60 points,
Goober with 45 points, and
Andy with 30 points.
Logic Sequence:
Clue #1. Barney scored 75 or 100; Goober scored 30 or 45.
Clue #2. Otis scored 45 or 75.
Clue #3. Bee scored 60 or 75, Andy scored 30 or 45.
By elimination, Bee scored 60.
Then, referring back to Clue #3, Andy scored 30.
By elimination, Goober scored 45, Otis scored 75, and Barney scored 100.