# solving a logic grid puzzle

This is a puzzle from mysterymaster.

Five students of twentieth-century literature (Oscar, Peter, Shirley, and two women named Ruth) elected to write their term papers each on a different work of fiction (including William Faulkner's Light in August and Katherine Anne Porter's Ship of Fools). One pair of students are siblings with the same last name, and the other three are unrelated. Can you deduce the full name of each student (at least one is surnamed Zaniewski), and the novel that each chose?

1. Shirley is an only child.
2. The two men are unrelated; exactly one of them chose a Faulkner novel.
3. The student (whose first name isn't Ruth) who chose Ernest Hemingway's The Sun Also Rises has a sibling in class.
4. The book chosen by the only student surnamed Yorke didn't have "light" anywhere in its title.
5. Four of the five students are Oscar, Ms. Underwood, the only student surnamed Valdez, and the one who chose Virginia Woolf's To the Lighthouse; the fifth student shares either a first name, last name, or choice of author with the person who chose William Faulkner's Absalom! Absalom!

I got the following from the clues: Oscar is not Valdez or Underwood and didnot read Virginia Woolf. Out of Oscar and Peter one chose Faulkner and one chose Hemmingway. Shirley is not a Zaniewski. Both the Ruths didnot read hemmingway. Peter and Oscar are not siblings. Yorke didnot read Woolf or Faulkner's Light in August. I am not able to proceed any futher to fix a clue. Do suggest the method and error in my deduction(if any).

• Not enough time to write out a solution at the moment, but just wanted to mention that you make an error in assuming that Oscar is not an Underwood, Underwood is one of the last names that can appear twice. Commented Mar 15, 2017 at 9:02
• I spent an hour on this, got stuck, went to the mysterymaster website, and subsequently got stuck for another hour trying to understand the app. I'm getting too old for this. Commented Mar 15, 2017 at 16:27

A. Forenames: Oscar, Peter, Shirley, Ruth, Ruth. Surnames: Zaniewski, Yorke, Underwood, Valdez, one of them (not Valdez) twice. Books: Faulkner's "Light in August" and "Absalom! Absalom!", Porter's "Ship of Fools", Woolf's "To the Lighthouse", Hemingway's "The Sun also Rises".

B. At least one of the siblings is a woman (by #2). The women are two Ruths and a Shirley, and Shirley isn't a sibling (by #1). So, assuming (I think fairly) that we don't have two siblings with the same forename as well as the same surname, the siblings are Ruth X and either Oscar X or Peter X. The latter must be the one in #3 who chose Hemingway's TSAR; then by #2 the other man chose something by Faulkner.

C. X (in B above) is not Yorke (by #4) nor Valdez (by #5) so it's either Underwood or Zaniewski.

D. Yorke chose a book without "light" (by #4). It wasn't TSAR because that was chosen by Oscar/Peter X (by B) and X is not Yorke (by C). So Yorke chose either Faulkner's "Absalom! Absalom!" or Porter's "Ship of Fools".

E. If Yorke chose "Absalom! Absalom!" then the fifth student mentioned in #5 shares Yorke's first name or author. (Not surname; by #4 there is only one Yorke.) If it's the first name then that name must be Ruth (by A) so that fifth student is Ruth X who has a sibling. In this case we have Ruth Yorke who chose AA; Ruth X; and Oscar/Peter X who chose TSAR. Then the other man chose a Faulkner novel, which (since Ruth Yorke isn't the other man) must have been LIA. Now return to #5; Ms. Underwood isn't Ruth Yorke, nor Ruth X (who is the "fifth student"), so must be Shirley. Also in the list in #5 is "the one who chose Virginia Woolf's To the Lighthouse"; that's not Ruth Yorke who chose AA, nor either of the men who chose Hemingway and Faulkner, so it's Ruth X. But wait!, Ruth X is the "fifth student" and we have a contradiction. So, unwinding, if Yorke chose "Absalom! Absalom!" then what the fifth student shares is Yorke's author, not Yorke's first name.

F. (Continuing the hypothesis from E.) In this case the "fifth student" chose the other Faulkner book, "Light in August". Now, where does Yorke appear in the list in #5? Not as "Ms. Underwood" (wrong surname) nor as "the only Valdez" (wrong surname) nor as "the person who chose TTL" (wrong book) nor as the "fifth student" (I take it the wording of #5 is meant to exclude cases where that student is the same person as the one they share whatever-it-is with); hence it's Oscar Yorke. Now, there's only one Yorke so (by B) our siblings are Ruth X and Peter X, and Peter chose "The Sun also Rises". But this is impossible, because from the list in #5 we have: Oscar Yorke (chose AA, hence not Peter X), Ms. Underwood (female, hence not Peter X), Valdez (only one of that surname, hence not Peter X), the person who chose "To the Lighthouse" (wrong book to be Peter X), and the fifth student (chose "Light in August", wrong book to be Peter X). So no one can be Peter X. So, unwinding, we have found that Yorke did not choose "Absalom! Absalom! and hence (by D) that Yorke chose "Ship of Fools".

G. OK, let's think more about Yorke. Yorke isn't either X (from B) because there is only one Yorke. Yorke is also not the man-who-isn't-an-X because he chose something by Faulkner (by B) but Yorke chose "Ship of Fools" (by F). So Yorke is either Ruth not-X or Shirley. Where does she fit into the list in #5? Not "Oscar" (wrong sex), nor "Ms. Underwood" (wrong surname), not "the only Valdez" (wrong surname), not "the one who chose TTL" (wrong book). So Yorke is the "fifth student".

H. What does Yorke, the fifth student, share with the person who chose "Absalom! Absalom!"? Not her surname (there is only one Yorke by #4) nor the author (Yorke chose Porter's "Ship of Fools"), hence her first name. The repeated first name is Ruth. So Ruth not-X is in fact Ruth Yorke; and the other Ruth -- who is Ruth X -- chose "Absalom! Absalom!" (So the not-X man who also chose Faulkner must have chosen "Light in August".)

I. Now, consider these three: Ruth X (Absalom! Absalom!), Oscar/Peter X (The Sun Also Rises), and Peter/Oscar not-X (Light in August). These must be the first three people in the list in #5, because the other two are known to have chosen other books: "the one who chose TTL" and the fifth student, who (by F,G) chose "Ship of Fools"). Two of these three are men, which means that Ms. Underwood must be Ruth X. So X = Underwood; Peter is Valdez; and Oscar is the other Underwood.

J. The remaining student -- the fourth in the list in #5 -- must therefore be Shirley Zaniewski.

So the final line-up is:

Oscar Underwood Hemingway The Sun Also Rises "Oscar" Ruth Underwood Faulkner Absalom! Absalom! "Ms. Underwood" Peter Valdez Faulkner Light in August "Valdez" Shirley Zaniewski Woolf To the Lighthouse "one who chose TTL" Ruth Yorke Porter Ship of Fools "fifth student"

and unless I have erred, all the given conditions hold as required.