Eight college students — Al, Ben, Jim, Keith, Pete, Sam, Rick, and Vince — occupy four rooms in the men’s dormitory — 201, 202, 203, and 204 — where they live two to a room. Four men are smokers, and four are non-smokers. Four men are engineering majors (chemical, electrical, aeronautical, and marine), and four are liberal arts majors (math, German, biology, and history). From the clues given, match the pairs of roommates by first and last names, room number, and major. (Last names are: Burns, Graham, Handley, Hunt, Johnson, Kelly, Rogers and Smith.)
1. The college never puts a smoker in the same room with a non-smoker.
2. The college always puts an engineering major in the same room with a liberal arts major.
3. The four smokers are: Vince, Mr. Graham, the electrical engineering major, and the liberal arts major in 201.
4. The four liberal arts majors are: Sam, the one in 204, Mr. Hunt, and Pete’s roommate.
5. Rick doesn’t smoke, doesn’t live in 202, and doesn’t room with the biology major or the marine engineering major (who doesn’t live in 202 either).
6. Al smokes and doesn’t major in math or aeronautical engineering.
7. Four different rooms are occupied by: Mr. Graham, the chemical engineering major, Mr. Kelly, and the math major.
8. Mr. Burns lives in 203 and is in liberal arts.
9. Exactly one student has the same first and last initials.
10. Pete is not the aeronautical engineering major, doesn’t smoke, and doesn’t live in 203.
11. The German major smokes and does not room with the electrical engineering major.
12. Jim is not Mr. Burns or Mr. Hunt; Mr. Handley is in liberal arts. Between Jim and Mr. Handley, one smokes and the other doesn’t.
13. Two non-smoking roommates are Mr. Smith and the history major.
14. The biology major’s room number is higher than Mr. Handley’s, which is higher than Mr. Kelly’s.
15. Either A or B is True, but not both:
A. Keith is Mr. Rogers.
B. Vince is Mr. Kelly.
16. Ben doesn’t smoke. Keith’s roommate is in liberal arts.
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