Open and Shut

pearson shutter puzzle

A poser by Cyril Pearson, puzzle editor for the London Evening Standard at the turn of the 20th century:

Upon the shutters of a barber’s shop the legend above was painted in bold letters. One evening about 8:30, when it was blowing great guns, quite a crowd gathered round the window, and seemed to be enjoying some excellent joke. What was amusing them when the shutter blew open?

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Babel on Olympus

In 1996, MIT philosopher George Boolos published this puzzle by Raymond Smullyan in The Harvard Review of Philosophy, calling it “the hardest logical puzzle ever”:

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

Boolos made three clarifying points:

  • It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
  • What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
  • Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

What’s the solution?

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Good Point

The people of Delos were arguing before the Athenians the claims of their country,– a sacred island, they said, in which no one is ever born and no one is ever buried. ‘Then,’ asked Pausanias, ‘how can that be your country?’

— F.A. Paley, Greek Wit, 1888

Business News

What’s unusual about this paragraph, composed by Lawrence Cowan?

Trade was arrested as a base act after federated reserves regressed faster as extracted free trade was saved as extra reverted waste. Deserted as better fates were created, a few brave castes feared effects as excess stargazers were severed. Statecraft fretted, staggered, braced as steadfast braggarts beat state stewards, stewardesses. Tested as a great craze, trade traversed war; zest was dead as a few eager asses abated better treats, detested street fracases. Facts were effaced as we attested a great faded age.

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Three Riddles

From Henry Dudeney’s 300 Best Word Puzzles:

  1. What is that from which you may take away the whole and yet have some left?
  2. What is it which goes with an automobile, and comes with it; is of no use to it, and yet the automobile cannot move without it?
  3. Take away my first letter and I remain unchanged; take away my second letter and I remain unchanged; take away my third letter and I remain unchanged; take away all my letters and still I remain exactly the same.
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Pillow Talk

In 1951 James Thurber’s friend Mitchell challenged him to think of an English word that contains the four consecutive letters SGRA. Lying in bed that night, Thurber came up with these:

kissgranny. A man who seeks the company of older women, especially older women with money; a designing fellow, a fortune hunter.

blessgravy. A minister or cleric; the head of a family; one who says grace.

hossgrace. Innate or native dignity, similar to that of the thoroughbred hoss.

bussgranite. Literally, a stonekisser; a man who persists in trying to win the favor or attention of cold, indifferent, or capricious women.

tossgravel. A male human being who tosses gravel, usually at night, at the window of a female human being’s bedroom, usually that of a young virgin; hence, a lover, a male sweetheart, and an eloper.

Unfortunately, none of these is in the dictionary. What word was Mitchell thinking of?

15 Puzzle

A problem from the 1999 Russian mathematical olympiad:

Show that the numbers from 1 to 15 can’t be divided into a group A of 13 numbers and a group B of 2 numbers so that the sum of the numbers in A equals the product of the numbers in B.

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