Short Orders

One afternoon the doorbell rang at Peter Sellers’ London flat. Sellers was working in his study upstairs, so his wife Anne answered the door. It was a telegram for her:


In 1960 Jerry Lewis and Henny Youngman were having lunch at a Miami restaurant when Lewis was mobbed by autograph seekers. Youngman slipped out to the lobby unnoticed and returned as if nothing had happened. Shortly afterward Lewis received a telegram from the hotel bellboy:


In a Word

adj. armed with a noose

adj. hanging from a rope

adj. pertaining to the gallows

On Feb. 23, 1885, convicted murderer John Lee of Devon was brought to the scaffold and positioned on the trapdoor. The noose was fitted around his neck, and executioner James Berry pulled the lever.

Nothing happened.

Two warders tried to force the trapdoor to open under Lee, but they failed. They removed the condemned man and tested the door, and it worked. So they put Lee in position again, and again Berry pulled the lever.

Again nothing happened.

Exasperated, the warders again put Lee aside and set to work on the door, this time with hatchets. When they were satisfied, they returned him to the scaffold, and Berry pulled the lever a third time.

Nothing happened.

So the Home Secretary commuted Lee’s sentence to life imprisonment.


The autobiography of the 12th-century Muslim poet Usama ibn Munqidh tells of an incident in which the invading Crusaders appealed for a doctor to treat some of their number who had fallen ill. The Muslims sent a doctor named Thabit, who returned after 10 days with this story:

They took me to see a knight who had an abscess on his leg, and a woman with consumption. I applied a poultice to the leg, and the abscess opened and began to heal. I prescribed a cleansing and refreshing diet for the woman. Then there appeared a Frankish doctor, who said: ‘This man has no idea how to cure these people!’ He turned to the knight and said: ‘Which would you prefer, to live with one leg or die with two?’ When the knight replied that he would prefer living with one leg, he sent for the strong man and a sharp axe. They arrived, and I stood by to watch. The doctor supported the leg on a block of wood, and said to the man: ‘Strike a mighty blow, and cut cleanly!’ … The marrow spurted out of the leg (after the second blow) and the patient died instantaneously. Then the doctor examined the woman and said: ‘She has a devil in her head who is in love with her. Cut her hair off!’ This was done, and she went back to eating her usual Frankish food … which made her illness worse. ‘The devil has got into her brain,’ pronounced the doctor. He took a razor and cut a cross on her head, and removed the brain so that the inside of the skull was laid bare … the woman died instantly. At this juncture I asked whether they had any further need of me, as they had none I came away, having learnt things about medical methods that I never knew before.


Travel due north, south, east, or west from Stamford, Conn., and you’ll find yourself in New York state.

Sweet Reason

A brainteaser by Chris Maslanka:

A packet of sugar retails for 90 cents. Each packet includes a voucher, and nine vouchers can be redeemed for a free packet. What is the value of the contents of one packet? (Ignore the cost of the packaging.)

Click for Answer

Afghan Bands

afghan bands

Most people know that if you cut a Möbius band in two lengthwise you’ll produce one band rather than two. But splitting the ends and joining them also creates some surprising effects.

Starting with the figure above, join ends A and D directly, then pass B under A and join it to E. Now pass C over B and under A; pass F over D and under E; and join C and F. Extend the slits along the length of the band and you’ll have three linked rings.

Now compare this variant, suggested by Ellis Stanyon in 1930: Starting again from the diagram, give E a half-twist to the right and join it to C; give F a half-twist to the right and join it to B; then pass A under B and join it to D (without turning it over). Cut along the two slits and you’ll produce a small ring linked to a large one. What became of the third ring?

There’s a surprisingly simple way to produce a similar effect: Draw a line along the length of a Möbius band, one-third of the way across the strip. Cutting along this line will produce a large band linked to a small one — and this time the small band is itself a Möbius band, on which you can repeat the feat.

You Answer Quite Slowly

What key is “Lucy in the Sky With Diamonds” written in? It’s not easy to say; the harmony is strangely ambiguous. Musicologist Naphtali Wagner found that the song is notated differently in two reasonably authoritative sources, Wise Publications’ The Beatles Complete (1983) and Hal Leonard’s The Beatles: Complete Scores (1993):

"lucy in the sky with diamonds" key signatures

And he found that scholars disagree as well:

  • Steven Porter believes that it’s in A major, “surrounded by tonicized structural neighbour tones (B♭ major and G major), as a sort of substitute for the absence of a structural dominant.”
  • Walter Everett believes it’s in G major, citing a voice-leading graph that opens with the hypothetical notes G and B in the outer voices.
  • Allan Moore is ambivalent: The scale steps in the upper voice suggest G major, but the bass line contradicts this, and the key signatures suggest D major.

Wagner shows that a case can be made for three rival interpretations: A major, D major, and G major. “Each is consistent with the Beatles’ harmonic style and has precedents in many other songs.” But he adds that one solution might be to abandon the idea of monotonality and see the song as oscillating between two keys: A in the chorus and pre-chorus and G in the chorus. “This version could be defended with the argument that oscillation between tonal centres separated by a major second is found in other Beatles songs, such as ‘Doctor Robert,’ ‘Good Day Sunshine’ and ‘Penny Lane.'”

(Naphtali Wagner, “The Beatles’ Psycheclassical Synthesis: Psychedelic Classicism and Classical Psychedelia in Sgt. Pepper,” in Oliver Julien, ed., Sgt. Pepper and the Beatles, 2008)


“My living in Yorkshire was so far out of the way, that it was actually twelve miles from a lemon.” — Sydney Smith


One day in 1880 John Muir set out to explore a glacier in southeastern Alaska, accompanied by Stickeen, the dog belonging to his traveling companion. The day went well, but on their way back to camp they found their way blocked by an immense 50-foot crevasse crossed diagonally by a narrow fin of ice. After long deliberation Muir cut his way down to the fin, straddled it and worked his way perilously across, but Stickeen, who had shown dauntless courage throughout the day, could not be convinced to follow. He sought desperately for some other route, gazing fearfully into the gulf and “moaning and wailing as if in the bitterness of death.” Muir called to him, pretended to march off, and finally ordered him sternly to cross the bridge. Miserably the dog inched down to the farther end and, “lifting his feet with the regularity and slowness of the vibrations of a seconds pendulum,” crept across the abyss and scrambled up to Muir’s side.

And now came a scene! ‘Well done, well done, little boy! Brave boy!’ I cried, trying to catch and caress him; but he would not be caught. Never before or since have I seen anything like so passionate a revulsion from the depths of despair to exultant, triumphant, uncontrollable joy. He flashed and darted hither and thither as if fairly demented, screaming and shouting, swirling round and round in giddy loops and circles like a leaf in a whirlwind, lying down, and rolling over and over, sidewise and heels over head, and pouring forth a tumultuous flood of hysterical cries and sobs and gasping mutterings. When I ran up to him to shake him, fearing he might die of joy, he flashed off two or three hundred yards, his feet in a mist of motion; then, turning suddenly, came back in a wild rush and launched himself at my face, almost knocking me down, all the while screeching and screaming and shouting as if saying, ‘Saved! saved! saved!’ Then away again, dropping suddenly at times with his feet in the air, trembling and fairly sobbing. Such passionate emotion was enough to kill him. Moses’ stately song of triumph after escaping the Egyptians and the Red Sea was nothing to it. Who could have guessed the capacity of the dull, enduring little fellow for all that most stirs this mortal frame? Nobody could have helped crying with him!

Thereafter, Muir wrote, “Stickeen was a changed dog. During the rest of the trip, instead of holding aloof, he always lay by my side, tried to keep me constantly in sight, and would hardly accept a morsel of food, however tempting, from any hand but mine. At night, when all was quiet about the camp-fire, he would come to me and rest his head on my knee with a look of devotion as if I were his god. And often as he caught my eye he seemed to be trying to say, ‘Wasn’t that an awful time we had together on the glacier?'”

The Pill Scale (Part 2)

A variation on yesterday’s puzzle:

Suppose there are six bottles of pills, and more than one of them may contain defective pills that weigh 6 grams instead of 5. How can we identify the bad bottles with a single weighing?

Click for Answer