Points of Pride

She’s the girl that makes the thing that drills the hole that holds the spring
That drives the rod that turns the knob that works the thingumebob,
And it’s the girl that makes the thing that holds that oil that oils the ring
That works the thingumebob THAT’S GOING TO WIN THE WAR!

— Popular song of 1942

“I’ve Danced With a Man, Who’s Danced With a Girl, Who’s Danced With the Prince of Wales”

— Popular song of 1927

Dr. Polycarp was, as you all know, an unusually sallow bimetallist. ‘There,’ people of wide experience would say, ‘There goes the sallowest bimetallist in Cheshire.’

— G.K. Chesterton, The Napoleon of Notting Hill, 1904

| Entertainment · History · Literature · Society

Query

From Gerald Lynton Kaufman’s The Book of Modern Puzzles (1954):

  1. All DROONS are the same size and shape.
  2. All green SLACKENS are the same size and shape.
  3. Twenty DROONS just fill up a MULDRUFF.
  4. All WALLAXES contain green SLACKENS.
  5. A green SLACKEN is 10% bigger than a DROON.
  6. A WALLAX is smaller than a MULDRUFF.

“If all MULDRUFFS and all WALLAXES are predominantly RED throughout, what is the largest possible number of green SLACKENS in a WALLAX?”

Click for Answer

Eight. If a MULDRUFF holds 20 DROONS, and a green SLACKEN is 10% bigger than a DROON, then a MULDRUFF can accommodate at most 18 green SLACKENS. And if a WALLAX is smaller than this, then it can hold at most 17 green SLACKENS. But if each WALLAX is predominantly red, then the proportion of green SLACKENS in its contents can’t be more than one-half. So the largest number of green SLACKENS it can contain is 8.

11/22/2025 UPDATE: This is just wrong. Let a DROON have size 1. Then a MULDRUFF has capacity 20, and a green SLACKEN has size 1.1. So our MULDRUFF will accommodate 9 green SLACKENs (= 9.9) and 10 DROONS (= 19.9 < 20). Now we can transfer this cargo to a WALLAX of, say, capacity 19.95 and fulfill the terms of the problem with 9 (not 8) green SLACKENS -- the WALLAX remains predominantly red by both number and volume. Thanks to everyone who wrote in about this. [/spoiler]

| Puzzles

“Hallelujah!”

“Hallelujah!” was the only observation
That escaped Lieutenant-Colonel Mary Jane,
When she tumbled off the platform in the station,
And was cut in little pieces by the train.
Mary Jane, the train is through yer:
Hallelujah, Hallelujah!
We will gather up the fragments that remain.

— A.E. Housman

| Poems

Impostor

https://commons.wikimedia.org/wiki/File:Cululus_canorus(1925).jpg

Visiting Hamburg in 1878, Mark Twain heard a cuckoo calling in the woods.

“First cuckoo I ever heard outside of a clock,” he wrote. “Was surprised how closely it imitated the clock — and yet of course it could never have heard a clock.”

He added, “The hatefulest thing in the world is a cuckoo clock.”

(From his Notebook.)

| Literature

Dead Letters

In 1814, as the British burned Washington, commander Sir George Cockburn targeted the offices of the National Intelligencer newspaper, telling his troops, “Be sure that all the C’s are destroyed, so that the rascals cannot any longer abuse my name.”

British politician Thomas Erskine (1750-1823) had such an enormous ego that, it was said, one newspaper had to curtail its coverage because its “stock of capital I’s was quite exhausted.”

| History · Language

Roundabout

https://commons.wikimedia.org/wiki/File:Stuber-Musique.jpg

Alsatian pastor J.G. Stuber composed this puzzle canon in the late 18th century.

“It was always a great delight to me, in riding my horse from one village to another, to hear in the fields and among the heights the melodies which I had taught,” he wrote. “I could often distinguish very beautiful and harmonious voices.”

| Art

All the Way Down

https://commons.wikimedia.org/wiki/File:Geometric_series_14_square2.svg

The infinite series 1/4 + 1/16 + 1/64 + 1/256 + … was one of the first to be summed in the history of mathematics; Archimedes had found by 200 BC that it totals 1/3. There are two neat visual demonstrations that make this fact immediately apparent. In the unit square above, the largest black square has area 1/4, the next-largest black square has area 1/16, and so on. Regions of black, white, and gray make up equal areas in the total figure, so the black squares, taken together, must have area 1/3.

The same argument can be made using triangles (below). If the area of the largest triangle is 1, then the largest black triangle has area 1/4, the next-largest 1/16, and so on. Areas of black, white, and gray make up equal parts of the total figure, so the black regions must total 1/3.

https://commons.wikimedia.org/wiki/File:Geometric_series_triangle.svg
Image: Wikimedia Commons
| Science & Math

Briefly

Asked whether he could summarize the lessons of history in a short book, Columbia historian Charles Beard said he could do it in four sentences:

  1. Whom the gods would destroy, they first make mad with power.
  2. The mills of God grind slowly, but they grind exceeding small.
  3. The bee fertilizes the flower it robs.
  4. When it is dark enough, you can see the stars.
| History · Quotations