Andy dislikes the catcher. Ed's sister is engaged to the second baseman. The center fielder is taller than the right fielder. Harry and the third baseman live in the same building. Paul and Allen each won $20 from the pitcher at pinochle. Ed and the outfielders play poker during their free time. The pitcher's wife is the third baseman's sister. The pitcher, catcher, and infielders except Allen, Harry, and Andy, are shorter than Sam. Paul, Andy, and the shortstop lost $50 each at the racetrack. Paul, Harry, Bill, and the catcher took a trouncing from the second baseman at pool. Sam is involved in a divorce suit. The catcher and the third baseman each have two children. Ed, Paul, Jerry, the right fielder, and the center fielder are bachelors. The others are married. The shortstop, the third baseman, and Bill each cleaned up $100 betting on the fight. One of the outfielders is either Mike or Andy. Jerry is taller than Bill. Mike is shorter than Bill. Each of them is heavier than the third baseman.
Using these facts, determine the names of the men playing the various positions on the baseball team.
Harry is the pitcher, Allen the catcher, Paul the first baseman, Jerry the second baseman, Andy the third baseman, Ed the shortstop, Sam the left fielder, Mike the right fielder, and Bill the center fielder.