The Heist

A puzzle by Jared Z., Nicole H., and Benjamin E., mathematicians at the National Security Agency:

The chief detective hurried down to the police station after hearing big news: there was a heist at Pi National Bank! The police had brought in seven known gang members seen leaving the scene of the crime. They belonged to the nefarious True/False Gang, so named because each member is either required to always tell the truth or required to always lie, although everyone is capable of engaging in wrongdoing. The chief also knew from his past cases that any crime committed by the gang always included one truth teller.

When the chief showed up, he asked the gang members the following questions:

1) Are you guilty?
2) How many of the seven of you are guilty?
3) How many of the seven of you tell the truth?

Here were their responses:

Person 1: Yes; 1; 1
Person 2: Yes; 3; 3
Person 3: No; 2; 2
Person 4: No; 4; 1
Person 5: No; 3; 3
Person 6: No; 3; 3
Person 7: Yes; 2; 2

After looking these answers over, the chief prepared to arrest those responsible.

Which of these seven did the chief arrest?

Click for Answer
| Puzzles

In a Word

condisciple
n. a fellow student

precariat
n. people whose living standards are insecure

scripturiency
n. passion for writing

refocillation
n. imparting of new vigor

This brass plate is displayed at the corner of Drummond Street and South Bridge, near Rutherford’s Bar, in Edinburgh:

https://www.geograph.org.uk/photo/1517098
Image: kim traynor

(Thanks, Nick.)

| Language · Literature

Yajilin

https://commons.wikimedia.org/wiki/File:Yajilin_puzzle_(vector).png
Image: Wikimedia Commons

The goal of this logic puzzle is simple: to draw an orthogonally connected, non-intersecting loop that passes through every white square on the board. The trouble is that the board contains some number of black squares, and these are hidden. The only clues to their location are the numbers in the gray squares. In the diagram above, there are exactly 3 black squares in the third file north of the “3” indicator. And there are no black squares on the third rank anywhere east of the “0” indicator.

Gray squares can’t be black, no two black squares are orthogonally adjacent, and there may be some black squares that aren’t referred to by any of the indicators.

Knowing all this (and knowing that a solution is possible), can you determine the location of all the black squares and draw a loop that passes through all the white ones?

Click for Answer
| Puzzles

Misc

  • Angkor Wat and Machu Picchu are roughly antipodal.
  • WONDER is UNDERWAY in Pig Latin.
  • By convention, current flows from positive to negative in a circuit; electrons, which are negatively charged, move in the opposite direction.
  • The immaculate conception describes the birth of Mary, not Jesus.
  • “A man’s style in any art should be like his dress — it should attract as little attention as possible.” — Samuel Butler

10/22/2024 UPDATE: Interesting addendum from reader Mark Thompson: The capital cities Asunción, Canberra, and Kuwait City are nearly equidistant on great-circle routes:

Kuwait City to Canberra: 12,768 km
Canberra to Asunción: 12,712 km
Asunción to Kuwait City: 12,766 km

“Their mutual distances apart (along the earth’s surface) happen to be very close to one Earth-diameter [12,742 km]: so, sadly, they don’t all lie on a single great circle (since pi is not 3).” (Thanks, Mark.)

| Language · Quotations · Religion · Science & Math · Trivia

Degrees of Variance

In a 2008 essay, computer scientist Paul Graham offered a hierarchy of verbal disagreement:

https://commons.wikimedia.org/wiki/File:Graham%27s_Hierarchy_of_Disagreement-en.svg
Image: Wikimedia Commons

“The most obvious advantage of classifying the forms of disagreement is that it will help people to evaluate what they read,” he wrote. “But the greatest benefit of disagreeing well is not just that it will make conversations better, but that it will make the people who have them happier. … If you study conversations, you find there is a lot more meanness down in [Name-Calling] than up in [Refuting the Central Point]. You don’t have to be mean when you have a real point to make.”

| Society

An Enigmatic Letter

In 1614, William Nealson, a trader in Japan for the British East India Company, wrote to his friend Richard Wickham. The first half of the letter is sensible enough, and Nealson notes that his associate Mr. Cocks has already written to Wickham, “wherein he hath informed you of all business, so as for me to write thereof should be but a tedious iteration.” But then he writes “Now to the purpose” and seems to go mad:

Concerning our domestic affairs, we live well and contentedly, and believe me, if you were here, I could think we were and should be a happy company, without strife or brawling. Of late I caught a great cold for want of bedstaves, but I have taken order for falling into the like inconveniences. For first, to recover my former health, I forgot not, fasting, a pot of blue burning ale with a fiery flaming toast and after (for recreation’s sake) provided a long staff with a pike in the end of it to jump over joined stools with. Hem.

Notwithstanding I may sing honononera, for my trade is quite decayed. Before I had sale for my nails faster than I could make them, but now they lie on my hand. For my shoes none will sell, because long lying abed in the morning saves shoe leather, and driving of great nails puts my small nails quite out of request, yea, even with my best customer; so that where every day he had wont to buy his dozen nails in the morning, I can scarcely get his custom once in two or three. Well this world will mend one day, but beware the grey mare eat not the grinding stone. I have had two satirical letters about this matter from Mr. Peacock, which pleased him as little as me, but I think he is so paid home at his own weapon as he will take better heed how he carp without cause. It was not more to me, but broader to Mr. Cocks. I know the parties which I speak of you would gladly know; for your satisfaction herein I cannot make you know mine, because I think you never see her; but I think God made her a woman and I a W. For the other, it is such a one as hardly or no I know you would not dream of. But yet for exposition of this riddle, construe this: all is not cuckolds that wear horns. Read this reversed, Ab dextro ad sinistro. O I G N I T A M. What, man! what is the matter? methinks you make crosses. For never muse on the matter; it is true. I am now grown poetical.

He that hath a high horse may get a great fall;
And he that hath a deaf boy, loud may he call;
And he that hath a fair wife, sore may he dread
That he get other folks’ brats to foster and to feed.

Is this code? Nealson closes by warning “Be not a blab of your tongue” and urges Wickham to destroy “whatever I write you of henceforward.” Are these inside jokes, or references to forgotten poems or songs? William Foster includes the letter without comment in his collection of correspondence received by the company. I haven’t been able to learn anything more about Nealson, or about this seeming oddity. I found it in Giles Milton’s Nathaniel’s Nutmeg (2012).

| Oddities

To Be Clear

Modern punctuation doesn’t always do the job, so writers have suggested various improvements. In the 1580s, English printer Henry Denham proposed a “percontation point,” ⸮, to be used at the end of a rhetorical question. In 1668, Anglican clergyman John Wilkins suggested using an inverted exclamation point, ¡, for the same purpose.

In the 1840s, Belgian newspaper publisher Marcellin Jobard introduced a small arrow whose orientation might indicate irony, irritation, indignation, or hesitation.

In 1899, French poet Alcanter de Brahm suggested a point d’ironie to indicate that a sentence was ironic or sarcastic:

https://commons.wikimedia.org/wiki/File:Ironie-Larousse-1897-p329.png

And in a 1966 essay, French writer Hervé Bazin proposed (left to right) the irony point, the doubt point, the conviction point, the acclamation point, the authority point, and the love point:

https://commons.wikimedia.org/wiki/Category:Proposed_punctuation_marks

None of these has caught on, but the interrobang, ‽, introduced in 1962 by Martin Speckter to denote a question expressed in an exclamatory manner, is still included in many fonts.

More at Type Talk.

| Language

Ghost Leg

Ghost leg is a method of establishing random pairings between any two sets of equal size. For example, it might be used to assign chores randomly to a group of people. The names of the participants are listed across the top of the diagram and the chores across the bottom, and a vertical line is drawn connecting each name to the chore below it. Then the names are concealed and each participant adds a “leg” to the diagram. A leg is a segment that connects two adjacent vertical lines (it must not touch any other horizontal line).

When the legs have been drawn, the names are revealed and a path drawn from each name to the bottom of the diagram. Each path must follow each leg that it encounters, jumping to the adjacent vertical line and continuing downward. When it reaches a chore at the bottom, it establishes a link between a name and a chore.

The benefit of this method is that it will work for groups of any size, reliably establishing a 1:1 correspondence between their elements. And it will work no matter how many horizontal lines are added. In Japanese it’s known as amidakuji.

https://commons.wikimedia.org/wiki/File:Amidakuji_en.svg

| Science & Math

Magic Square Hereabouts

sallows non-atomic square

From Lee Sallows:

A feature common to many geomagic squares is that the set of shapes they employ reveal an atomic structure. That is, they are built up from repeated copies of a single unit shape. Examples of this are piece sets composed of polyominoes, the unit shape then being a (relatively small) square.

For the would-be geomagic square constructor, a key advantage of the atomic property is that the shapes concerned are each describable in terms of the positions of their constituent atoms. Or, to put it another way, they can be represented by a set of numbers. Hence, unlike non-atomic shapes, they are readily amenable to analysis and manipulation by computer.

Take, for example, an algorithm able to identify and list each of the different ways in which a given planar shape can be tiled by some specified set of smaller shapes. Such a program might be challenging to write, but provided the pieces concerned are composed of repeated units, implementation ought to be straightforward. But could the same be said in the case of non-atomic pieces? Without a set of numbers to describe piece shapes, how are they to be represented in a digital computer?

This is worth noting since, as inspection will show, the shapes employed in the square above are plainly non-atomic. In line with this I can confirm that the only computer program involved in deriving this solution was a vector graphics editor used to create the drawing seen above.

(Thanks, Lee.)

| Science & Math