Logic Problem 1
Solution:

 

The first person to play wasn't Michael (clue 1), Hunter (clue 2), Courtney or Jeff (clue 3), or Larry or Heidi (clue 4); she is Susan. By clue 2, Hunter was second and Mame was played 3rd. Since Susan didn't play Fiorello or Follies (clue 1), Nine (clue 3) or Hair or Annie (clue 4), she played the Cats album. The 7th player didn't play Fiorello or Follies (clue 1), Nine (clue 3) or Hair (clue 4), so the 7th player played Annie. By clue 4, then Heidi was 7th, Larry was 6th, and Hair was played 5th. Larry didn't play Fiorello (clue 1) or Nine (clue 3); he played Follies. By clue 1, the Fiorello album was 4th and Michael was 5th. By elimination, the Nine album was played second. By clue 3, Courtney was 3rd and Jeff was 4th.

 

 

 

 

 

Results:
Jeff, Fiorello, 4th
Hunter, Nine, 2nd
Susan, Cats, 1st
Heidi, Annie, 7th
Courtney, Mame, 3rd
Larry, Follies, 6th
Michael, Hair, 5th