Old Blue Eyes — A Logic Game
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Old Blue Eyes
Seven singers—Hiroshi, Jordan, Kirkwood, Lewin, Marin, Olin, and Pan—will audition for the lead singer role in a Frank Sinatra cover band. The auditions will take place one at a time, and no other singers will audition for the role. The order of the auditions must conform to the following rules:
- Exactly two auditions will take place between Jordan’s audition and Olin’s audition.
- Exactly one audition will take place between Marin’s audition and Pan’s audition.
- Hiroshi’s audition will take place immediately before or immediately after Lewin’s audition.
- Jordan’s audition will take place before Hiroshi’s audition.
1. Which one of the following could be the order of auditions, listed from first to last?
(A) Jordan, Lewin, Hiroshi, Olin, Marin, Kirkwood, Pan
(B) Jordan, Hiroshi, Lewin, Olin, Marin, Pan, Kirkwood
(C) Olin, Hiroshi, Lewin, Jordan, Pan, Kirkwood, Marin
(D) Pan, Olin, Marin, Jordan, Kirkwood, Hiroshi, Lewin
(E) Marin, Jordan, Pan, Lewin, Olin, Hiroshi, Kirkwood
2. If Olin auditions first, which one of the following must be true?
(A) Marin auditions third.
(B) Pan auditions third.
(C) Kirkwood auditions second.
(D) Jordan auditions third.
(E) Hiroshi auditions seventh.
3. If Lewin auditions immediately before Olin, each of the following could be true EXCEPT:
(A) Kirkwood auditions second.
(B) Marin auditions seventh.
(C) Pan auditions third.
(D) Jordan auditions first.
(E) Hiroshi auditions third.
4. If Kirkwood auditions sometime between Jordan and Olin, which one of the following must be true?
(A) Kirkwood auditions second.
(B) Either Marin or Pan auditions fifth.
(C) Either Marin or Pan auditions first.
(D) Either Hiroshi or Lewin auditions last.
(E) Jordan auditions either first or fourth.
5. There are exactly two possible orders of auditions if which one of the following is true?
(A) Hiroshi auditions immediately after Jordan.
(B) Kirkwood auditions immediately after Olin.
(C) Lewin auditions immediately after Olin.
(D) Marin auditions immediately after Jordan.
(E) Pan auditions immediately before Olin.
6. If Marin auditions first, which one of the following must be true?
(A) Kirkwood auditions before Pan.
(B) Olin auditions after Pan.
(C) Hiroshi auditions after Kirkwood.
(D) Lewin auditions before Olin.
(E) Jordan auditions after Kirkwood.
7. If the condition that Hiroshi’s audition will take place immediately before or immediately after Lewin’s audition is replaced with the condition that exactly one audition takes place between Hiroshi and Lewin, and if all other conditions remain in effect, each of the following could be true EXCEPT:
(A) Olin auditions fourth.
(B) Jordan auditions third.
(C) Kirkwood auditions first.
(D) Lewin auditions sixth.
(E) Hiroshi auditions fourth.
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