An Invitation

On Nov. 25, 1862, Abraham Lincoln sent this dispatch to Gen. Ambrose Burnside at Aquia Creek, Va.:

Can Inn Ale me withe 2 oar our Ann pas Ann me flesh ends NV Corn Inn out with U cud Inn heaven day nest Wed roe Moore Tom darkey hat Greek Why Hawk of abbott Inn B chewed I if.

What did it mean?

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In 1887, Irish journalist Richard Pigott sold a series of letters to the Times of London. Purportedly written by Irish Parliamentary Party leader Charles Parnell, they seemed to show that Parnell had approved of a savage political assassination five years earlier. Parnell denounced the letters as a “villainous and bare-faced forgery.”

In the ensuing investigation, Parnell’s attorney asked Pigott to write a series of words and submit them to the court:

Richard Pigott
Patrick Egan
P. Egan

What was the point of this?

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Black and White

ognjanovic chess problem

By Zarko Ognjanovic, 1912. White to mate in two moves.

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Buoy Howdy

From Russian puzzle maven Boris Kordemsky:

Two diesel ships leave a pier at the same time. One travels upstream, the other downstream, each with the same motive power. As they depart, one drops a lifebuoy into the water. An hour later, both ships reverse course. Which will reach the buoy first?

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Square Dance

paint scheme puzzle

From the 2001 Moscow Mathematical Olympiad:

Two stones, one black and one white, are placed on a chessboard. A move consists of moving one stone up, down, left, or right. The two stones may not occupy the same square. Does a sequence of moves exist that will produce every possible arrangement of the stones, each occurring exactly once?

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The Puzzle of the Self-Torturer

You’re fitted with a watch that imparts an electric current to your skin in increments too small to distinguish. Initially it’s set to 0 (off), and the settings run up to 1000. At the start of each week you’re allowed a period of experimentation to compare various settings, and then the watch is returned to its last setting. Then you have the option to increase the setting by 1; if you do this, you get $10,000. You may never reduce the setting.

What should you do? On the first day your experimentation shows you that the highest setting is completely intolerable; at that setting you’d pay any amount of money to get rid of the watch. But on this first week your decision is simply whether to advance from 0 to 1, getting $10,000 for accepting an imperceptible amount of pain. That seems attractive.

The trouble seems to be that your evaluations are “transitive” only at a large scale. If you prefer 0 to 500 and 500 to 1000, then it’s valid to conclude that you’ll prefer 0 to 1000. But if you prefer 51 to 4 (because of the financial reward) and 103 to 51, can we conclude that you’ll prefer 103 to 4? Not necessarily.

Unfortunately for all of us, this describes a lot of life. “The self-torturer is not alone in his predicament,” writes philosopher Warren S. Quinn, who proposed this puzzle in 1990. “Most of us are like him in one way or another. We like to eat but also care about our appearance. Just one more bite will give us pleasure and won’t make us look fatter; but very many bites will. And there may be similar connections between puffs of pleasant smoking and lung cancer, or between pleasurable moments of idleness and wasted lives.” What’s the best course?

(Warren S. Quinn, “The Puzzle of the Self-Torturer,” Philosophical Studies, May 1990)

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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Black and White

von wardener chess problem

By Friedrich Freiherr Von Wardener, 1904. White to mate in two moves.

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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