by Peter Turchi
SOLUTIONS
THE ONE WHO ALWAYS LIES, THE ONE WHO ALWAYS TELLS THE TRUTH
You point to one of the roads and ask one of the twins, “If I were to ask you if this road leads to town, would you say yes?” If it does, the truth-telling twin will say yes; if it doesn’t, she’ll say no. Similarly, if the road does lead to town, the liar will say no if asked directly, so she’s forced to lie and say yes. If the road doesn’t lead to town, she, too, needs to say no. (The more I think about it, the less likely it seems that this question ever appeared on the GRE. No doubt I was introduced to it by my puzzle-loving junior high math teacher, Gordon Culbertson.)
THE GENDER ELEVATOR
After the elevator stops at the fifth floor, it will hold two men and two women.
THE BOY, THE FOX, THE CHICKEN, AND THE BAG OF CORN
The boy takes the chicken across the river (this fox doesn’t eat corn), leaves the chicken on the other side, and goes back across. The boy then takes the fox across the river, and since he can’t leave the fox and chicken together, he brings the chicken back. Since the chicken and corn can’t be left together, he leaves the chicken and he takes the corn across and leaves it with the (crippled? tame?) fox. He then returns to pick up the chicken and crosses the river one last time, vowing to build a bigger raft.
THE REUNION OF THE FIVE POETS
If you haven’t solved one of these in a while, it’s helpful to build a grid that looks something like the one below.
To see the solution, go to the end of the solutions for this chapter.
WORD SQUARE BEGINNING WITH “CUBE”
This puzzle comes from Martin Gardner’s The Colossal Book of Short Puzzles and Problems, pages 403–4. One of many possible solutions is shown at left.
SUDOKU SOLUTION
ACROSTIC
Readers are invited to submit solutions to the puzzle on pages 28 and 29, created by Michael Ashley for this book. Correct solutions will be chosen at random to win a variety of prizes. For full details visit www.tupress.org/books/a-muse-and-a-maze.
THE FOUR LOGICAL WRITERS
This is a very slight modification of the classic Four Prisoners Problem, which came up during conversation at a lovely pre-wedding dinner outside of Florence, Italy. It assumes not only that the three people sitting in a row are perfectly logical but that they can rely on each other to be perfectly logical. If there are three writers for whom this is true, I haven’t met them. But: if the writer sitting behind her two friends sees that they both have red books on their heads, she knows hers is black; if she sees that they both have black books on their heads, she knows hers is red. If she sees that one has a black book and one has a red book, she knows better than to guess; and the writer sitting in front of her, understanding what her silence means—that he and the first writer in the row have different colored books on their heads—knows the color of his book is not the color of the one he can see in front of him.
THE REUNION OF THE FIVE POETS
The author of Two Cheeks is Alex, who drinks Malbec and writes limericks; the author of One Moon is Edna, who drinks scotch and writes sestinas; the author of My Thoughts is Louise, who drinks gin and writes sonnets; the author of Surging Tides is Walt, who drinks water and writes villanelles; and the author of Mist Shifts in Fits is Elizabeth, who drinks apple martinis and writes haiku.
2. How, from Such Wreckage, We Evolve the Eventual Effect
John Ruskin is quoted from his book The Elements of Drawing, in Three Letters to Beginners; the (corrected) larger Franklin Magic Square and a more complete discussion of its remarkable properties can be found under “Franklin’s Magic Squares” at mathpages.com; the Chart of the Gulfstream, credited to Benjamin Franklin and James Poupard, American Philosophical Society, Philadelphia, 1786?, appears courtesy of the Library of Congress; Raymond Chandler is quoted from his essay “The Simple Art of Murder” from The Simple Art of Murder, copyright © 1950 by Raymond Chandler, renewed © 1978 by Helga Greene, reprinted by permission of Houghton Mifflin Harcourt Publishing Company, all rights reserved; Anton Chekhov is quoted from his January 14, 1887, letter to Maria V. Kiseleva and, later, from an October 27, 1888, letter to Alexi S. Suvorin, both reprinted in Anton Chekhov and His Times, which also includes the reminiscence by Olga Knipper-Chekhova, “About A. P. Chekhov”; Ross MacDonald is quoted from Self-Portrait: Ceaselessly into the Past; the photo of a reproduction of the Turk appears courtesy of its creator, John Gaughan; Vladimir Nabokov is quoted from the transcript of his interview with BBC Television in 1962 and later from a 1964 interview with Playboy, both published in Strong Opinions; the photograph of Jim Sanborn’s Kryptos is courtesy of the artist; Teller is quoted from “Teller Reveals His Secrets,” published in Smithsonian Magazine, March 2012; Sir Arthur Conan Doyle is quoted from his brief and surprising BBC interview of May 14, 1930, courtesy of the Conan Doyle Estate Ltd.; Chekhov’s “Criminal Investigator” is in A Night in the Cemetery: And Other Stories of Crime and Suspense. Tim O’Brien is quoted from his essay “The Magic Show,” in Writers on Writing: A Bread Loaf Anthology, ed. Robert Pack and Jay Parini; Georges Perec is quoted from his “Thoughts on the Art and Technique of Crossing Words,” trans. Henri Picciotto with Arthur Schulman, reprinted in the Believer in September 2006; Steve Hodges discusses Perec’s use of the Knight’s Tour in his thesis “The Digital Absurd,” available at https://smartech.gatech.edu/bit-stream/handle/1853/33950/hodges_steven_201005_phd.pdf; the image of the tour was redrawn by Daniel Thomasson on his site Borderschess.org, which includes various Knight’s Tour puzzles; the Perec quotation comes from Oulipo Compendium; Matthew Gidley is quoted from his essay “Georges Perec and the Oulipians,” in frieze.com, 53, June–August 2000; the image of books playing chess is Your Move, Jonathan Wolstenholme, 2003, watercolor on paper, private collection, © Portal Painters/The Bridgeman Art Library; the 1613 map of Königsberg by Joachim Bering can be found on WikiCommons at http://commons.wikimedia.org/wiki/file:Koenigsberg,_Map_by_Bering_1613.jpg.
SOLUTIONS
First, a hint for the second cryptogram: the author’s name, following the quotation, is two words of nearly equal length.
CRYPTOGRAM
“I wish I could write as mysterious as a cat.”—Edgar Allan Poe
SECOND CRYPTOGRAM
“Why do people always expect authors to answer questions? I am an author because I want to ask questions. If I had answers I’d be a politician.”—Eugène Ionesco. And if that was too easy: this cipher is based on several key words—specifically, on the titles of four of Ionesco’s plays. By writing out the alphabet A–Z, and then writing out the substituted letters in sequence, you should—well, might—be able to identify those plays. Remember, repeated letters are omitted. The play titles are at the end of this chapter’s solutions.
ANIMAL CRACKERS
By Emily Cox and Henry Rathvon. Copyright © 2002 by American Crossword Puzzle Tournament (www.crosswordtournament.com). Used with permission.
MISSING DIGIT?
was created by Thomas Snyder, three-time world sudoku champion and the author of many puzzle books, including Sudoku Masterpieces, Battleship Sudoku, and Mutant Sudoku. For more variations on the form, see his Grandmaster Puzzles at gmpuzzles.com.
WILL SHORTZ’S ALPHABETICAL SETS
1. Tuesday
2. Jupiter
3. Clinton
4. Antarctica
5. Cupid
6. Nickel
7. Esther
8. Scorpio
9. Center field
10. Four of a kind
11. Doc
12. French hens
TWISTER
by Thomas Snyder, at right.
THE SEVEN BRIDGES OF KÖNIGSBERG
That single continuous walk which involves crossing each bridge once and only once isn’t possible, but not because of the number of bridges. The key is the number of bridges that attach to each land mass. A graph of the problem would look like the diagram at bottom right.
> Mathematicians refer to the bridges, or connections, as edges; they refer to the land, or connecting points, as nodes. Assuming all the nodes are connected, it turns out that, no matter how many bridges and connecting land masses are involved, if zero or two of the nodes have an odd number of edges, the single continuous circuit can be completed; in any other instance, it can’t. Since Königsberg’s four land masses were each accessed by an odd number of bridges, the walk was impossible.
THE IONESCO CIPHER
is thebaldprimoncsxkgjufqvwyz, which represents The Bald Prima Donna, Rhinoceros, Exit the King, and Jack, or The Submission, followed by the six unused letters of the alphabet.
3. Seven Clever Pieces
For more on the history of jigsaw puzzles, see Anne D. Williams’s The Jigsaw Puzzle: Piecing Together a History; the image of the Spilsbury puzzle is copyright © The British Library Board Maps 188.v.12.; Jan Kjærstad is quoted from The Seducer; the screen shots from Citizen Kane, originally released by RKO Pictures in 1941, are from the 70th Anniversary Edition; Martin Scorsese is quoted from the article “Within Him, Without Him,” by Dave Itzkoff, published in the New York Times, September 23, 2011; Tim O’Brien is again quoted from his essay “The Magic Show”; Charles Ritchie’s Twilight (1999; litho crayon, conte crayon, pen and ink, watercolor, graphite, silver ink, and collage on Fabriano paper; sheet/image 4 7/8 × 30 inches; private collection), Blue Twilight drawing (1996–97; graphite, watercolor, pastel, conté crayon, and litho crayon on Fabriano paper; sheet/image 22 × 30 inches; University of Richmond, Virginia), Blue Twilight print (2000–2001; dark-manner aquatint on heavyweight Rives BFK paper; image 10 15/16 × 14 7/8 inches, sheet 15 1/4 × 18 1/4 inches; published by Center Street Studio, Milton, Massachusetts), and Self-Portrait with Night I (2000–2002; watercolor, litho crayon, gouache, pen and ink, and graphite on Fabriano paper; sheet/image 5 1/8 × 11 7/8 inches; private collection) are reproduced here by permission of the artist; Stephen Greenblatt is quoted from Will in the World; excerpts from The Great Gatsby, by F. Scott Fitzgerald, are reprinted with the permission of Scribner Publishing Group, copyright © 1925 by Charles Scribner’s Sons, renewed © 1953 by Frances Scott Fitzgerald Lanahan, all rights reserved; the photographs of Anish Kapoor’s Memory appear courtesy of the artist and Deutsche Guggenheim (2008; Corten steel, 4.48 × 8.97 × 14.5 meters; installation view, Guggenheim New York, 2009; copyright © 2014 Anish Kapoor/ARS, New York/DACS, London); the page from Fun Home: A Family Tragicomic is copyright © 2006 by Alison Bechdel, reprinted by permission of Houghton Mifflin Harcourt Publishing Company, all rights reserved; James Salter is quoted from A Sport and a Pastime; the first two photographs of Markus Raetz’s Head appear courtesy of Vegar Moen/Artscape Nordland (1992; iron and granite; height 178 cm; Vestvågøy Municipality), while the third image is from a home video (see www.peterturchi.com). Finally, for a related discussion on characterization, see Steven Schwartz’s essay “The Absence of Their Presence: Mythic Character in Fiction,” in A Kite in the Wind.
SOLUTIONS
4. The Treasure Hunter’s Dilemma
The iconic 1899 photograph of Houdini in chains is courtesy of the Library of Congress, McManus-Young Collection; Hermann Hesse is quoted from his Autobiographical Writings; the poster of Houdini’s Death-Defying Mystery is from the Harry Ransom Center, the University of Texas at Austin; most of the information on Houdini, the Proteus Cabinet, and the disappearing elephant illusion are from Jim Steinmeyer’s Hiding the Elephant: How Magicians Invented the Impossible; the illustrations of the Proteus Cabinet and the elephant illusion are by Allegra Hyde, based on Steinmeyer’s originals; Dylan on Rimbaud is quoted from Bob Dylan: The Never Ending Star by Lee Marshall; the Thomas Wolfe quotation appears in David Herbert Donald’s Look Homeward: A Life of Thomas Wolfe; Louise Glück is quoted from Proofs and Theories; The Wizard of Oz was released in 1939 by Metro-Goldwyn-Mayer; Flannery O’Connor is quoted from Mystery and Manners; Bruce Springsteen is quoted in “Bringing It All Back Home,” by David Fricke, Rolling Stone, February 5, 2009; Joseph Conrad is quoted from “A Familiar Preface, 1912,” in A Personal Record; the quotations from Charles Ritchie are from personal interviews and the exhibition catalog Suburban Journals: The Sketches, Drawings, and Prints of Charles Ritchie; Ritchie’s Erased Self-Portrait (1983; watercolor, graphite, and pen and ink on Fabriano paper; sheet/image 7 × 4 inches; The Cartin Collection, Hartford, Connecticut) is reproduced here by permission of the artist; Van Gogh’s Chair (1888) is in the National Gallery, London; The Empty Chair, Gad’s Hill, 9th June, 1870 is by Sir Samuel Luke Fildes, oil on canvas, Rare Book Department, Free Library of Philadelphia/The Bridgeman Art Library; Dorothy Parker is quoted from her review “A Book of Great Short Stories,” in the New Yorker, October 29, 1927; Ernest Hemingway is quoted from an August 1924 letter to Gertrude Stein that appears in Ernest Hemingway: Selected Letters, 1917–1961; the Whitman lines beginning “From behind the screen” are from “So Long”; Charles Ritchie’s Self-Portrait with Paper Whites (1994–98; watercolor, graphite, and pen and ink on Fabriano paper; sheet/image 4 1/4 × 3 inches; private collection) and Kitchen Windows with Reflections (2011; watercolor and graphite on Fabriano paper; sheet/image 4 × 6 inches; collection of the artist) are reproduced here by permission of the artist; Evert A. Duyckinck is quoted from “Melville’s Moby-Dick; or, The Whale,” which originally appeared in New York Literary World 9 on November 22, 1851; Justin Kaplan is quoted from his book Mr. Clemens and Mark Twain: A Biography; the Twain-Howells letter is quoted by Jonathan Raban in his introduction to the Library of America paperback edition of Life on the Mississippi; Jonathan Raban is quoted from same; John Updike is quoted from “The Short Story and I,” in More Matter: Essays and Criticism; David Shields is quoted from “An Interview with David Shields,” Writer’s Chronicle, May 2004; the reproduction of the poster “Europe’s Eclipsing Sensation” is courtesy of Photofest; Ellen Bryant Voigt is quoted from “Song and Story,” an interview with Steven Cramer in the Atlantic, November 24, 1999; Norman Rockwell’s Triple Self-Portrait, illustration provided by Curtis Licensing, for all nonbook uses © SEPS, all rights reserved, printed by permission of the Norman Rockwell Family Agency, copyright © the Norman Rockwell Family Entities.
5. The Line, the Pyramid, and the Labyrinth
Wassily Kandinsky is quoted from his book Point and Line to Plane; the Ladders to Salvation game board image is taken from WikiCommons, http://en.wikipedia.org/wiki/File:Snakes_and_Ladders.jpg; John McPhee is quoted from his essay “Structure,” in the New Yorker, January 14, 2013; Walt Whitman is quoted from “Song of the Rolling Earth”; the image of the game board is by Allegra Hyde; Homer is quoted from the first lines of The Odyssey; Rudolf Arnheim is quoted from Art and Visual Perception; all the quotations of Tim Ingold, the discussion of reindeer hunters, and the Khanty storytellers are drawn from his book Lines: A Brief History; the picture of the garden path is copyright © Derek Fell, reprinted with permission; St. Jerome in the Wilderness (detail) is by Albrecht Dürer, c. 1496, engraving, private collection, The Bridgeman Art Library; John Ruskin is quoted from The Elements of Drawing; Henry Ernest Dudeney’s puzzles appear in The Canterbury Puzzles, and Other Curious Problems (1907); “Petie Pete versus Witch Bea-Witch” is from Italian Folktales, selected and retold by Italo Calvino, translated by George Martin, copyright © 1956 by Guilio Einaudi editore, s.p.a., English translation copyright © 1980 by Houghton Mifflin Harcourt, reprinted by permission of Houghton Mifflin Harcourt Publishing Company, all rights reserved; the leaping dancer and the following images are from Kandinsky’s Point and Line to Plane; the image of the Chartres labyrinth is from EcOasis/Shutterstock.com; maze by Dave Phillips, www.davephillipspuzzlemaze.com; the drawing of The Man in the Maze is by Allegra Hyde; Alice Munro’s “Royal Beatings” appears in her collection Who Do You Think You Are?; Michael Ondaatje is quoted from his Divisadero; the map of the caves of Crete is taken from Lines: A Brief History, was drawn by F. W. Sieber, and is in the Historic Collection
s, Kings College, University of Aberdeen; and Jonathan Raban is quoted once again from his introduction to Life on the Mississippi.
SOLUTIONS
THE PARDONER’S PUZZLE
6. The Pleasures of Difficulty
Mark Twain is quoted from the previously mentioned introduction by Jonathan Raban; Chekhov is quoted from his October 27, 1888, letter to Alexei S. Suvorin, reprinted in Anton Chekhov and His Times; “The Miller’s Puzzle” appears in Henry Ernest Dudeney’s The Canterbury Puzzles, and Other Curious Problems; Antonya Nelson’s “Strike Anywhere” appears in her collection Some Fun and, accompanied by her discussion of the story’s evolution, in The Story Behind the Story; James Salter is quoted from Solo Faces; Charles D’Ambrosio’s “The Scheme of Things” appears in his collection The Dead Fish Museum; David Jauss’s essay “What We Talk About When We Talk About Flow” appears in his collection Alone with All That Could Happen, republished as On Writing Fiction; Jesse Schell’s flow charts are reprinted from The Art of Game Design; the two drawings of stepping stones are by Allegra Hyde; the photo believed to be of Buddy Bolden’s band is reproduced here courtesy of the New Orleans Jazz Club Collection of the Louisiana State Museum; the sonograph image is reproduced from Michael Ondaatje’s Coming Through Slaughter; Whitman is quoted from an unpublished introduction dated May 31, 1861; Tony Hoagland is quoted from “Pinsky, Hass, Glück, and the Deployment of Talent,” in Real Sofistikashun: Essays on Poetry and Craft; Marin Alsop is quoted from her piece on Mahler for National Public Radio on February 9, 2007, available at npr.org; Mahler is quoted from a letter dated February 8, 1911, to Georg Goehler, in Selected Letters of Gustav Mahler, ed. Knud Martner; the Herbert von Karajan quote is attributed to him in many places but the actual source is unclear; ditto the later Mahler quotation; Andrew Wiles is quoted from Fermat’s Last Theorem.