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“We discover in ourselves what others hide from us, and we recognize in others what we hide from ourselves.” — Vauvenargues

A problem from the January-February 1991 issue of Quantum: Prove that the area of the yellow rectangle is half that of the full octagon.

Apocryphal but entertaining: Allegedly the Duke of Wellington sent this letter to the British War Office during the Peninsular War of 1808-1814: Gentlemen: Whilst marching to Portugal to a position which commands the approach to Madrid and the French forces, my officers have been diligently complying with your request which has been sent by H. M. ship from London to Lisbon and then by...

Thomas Taverner published this remarkable problem in the Dubuque Chess Journal in 1889. White is to mate in two moves.

Sir, The hymn ‘Onward Christian Soldiers’, sung to the right tune and in a not-too-brisk tempo, makes a very good egg timer. If you put the egg into boiling water and sing all five verses and chorus, the egg will be just right when you come to Amen. — Mrs. G.H. Moore, letter to the Daily Telegraph, 1983

Writing home from Princeton in 1939, 21-year-old Richard Feynman challenged his father to solve “this problem in long division. Each of the dots represents some digit (any digit). Each of the A’s represent the same digit (for example, a 3). None of the dots are the same as the A (i.e., no dot can be a 3 if A is 3).” We don’t know...

Psychoanalyst Robert Lindner received a remarkable client at his Baltimore practice: “Kirk Allen” had read a series of science fiction novels and “In some weird and inexplicable way I knew that what I was reading was my biography.” (Lindner never revealed which series this was, but some have theorized that it was the Barsoom books of Edgar Rice Burroughs, which describe the adventures of...

A popular mathematical puzzle asks: Suppose Earth were perfectly spherical and wrapped with a string at the equator. If we wanted to raise the string 1 meter off the ground, all around the world, how much longer would it need to be? Surprisingly, the answer is only about 6.3 meters. A circle of radius r has a circumference of 2πr. We’re adding a meter...

Two sadistically addressed letters, from the Strand, August 1897: “The accompanying envelope looks hopeless at first glance. It is a fair sample of the kind of thing which is specially invented to try the patience of the splendid staff of officials at the G.P.O. Hold it horizontally, on a level with the eyes, and you will read the address: ‘Miss J. M. Holland, Albion...

Is Dracula Moriarty? Is Holmes Van Helsing? In an article in the Baker Street Journal Christmas Annual of 1957, William Leonard points out that the events of Bram Stoker’s novel unfold between May and November 1890, a period in which Watson records only three cases with Sherlock Holmes. Stoker’s novel cites several news accounts about the growing mystery, which would certainly have attracted Holmes’...

The infinite monkey theorem holds that a monkey typing at random for an infinite amount of time will almost certainly produce the works of Shakespeare. This may be true, but mathematicians Stephen Woodcock and Jay Falletta of the University of Technology Sydney find that it would take an extraordinarily long time — longer, in fact, than the life span of the universe. Assuming a...

This unusual memorial stands in the New Forest National Park near Lyndhurst, Hampshire. At the start of World War I, manpower shortages prevented England from importing enough Canadian timber to supply the war’s needs, so English forests had to be felled to meet the requirement. The local foresters were away fighting, so a Portuguese Army unit with the Canadian Timber Corps lent its aid....

If I take a single glance at a speckled hen, I know that I’ve seen many speckles, but I can’t say how many I’ve seen. I have immediate experience of a determinate fact, but the experience doesn’t provide certain knowledge of the fact. “[O]ur difficulty is not that there must be characteristics of the many-speckled datum which pass unnoticed,” writes philosopher Roderick Chisholm. “[I]t...

Before 1963, hungry squirrels in Longview, Washington, had to leave their park and run across Olympia Way to collect nuts near a local office building. After seeing many of them killed, resident Amos Peters built a dedicated 60-foot bridge above the road. It’s now listed on the National Register of Historic Places.

Three girls dressed up in white, green, and blue dresses. They also wore shoes of these three colors. Only Ann wore a dress of the same color as her shoes. Neither Betty’s dress nor her shoes were white, and Carol’s shoes were green. What was the color of each girl’s dress?

Richard Jefferies’ 1885 novel After London is one of the first post-apocalypse stories, an adventure tale set in a future England after an unspecified catastrophe has destroyed civilization, cut off communication with the continent, and set the surviving human population back to a quasi-medieval existence among the overgrown ruins of the “ancients.” The nature of the disaster is never explained, but it must have...

In 1784, in the margin of a math notebook, English schoolboy Richard Beale drew a chicken wearing trousers. The Museum of English Rural Life tweeted the find after acquiring 41 Beale family diaries in 2016. Program manager Adam Koszary told the Guardian, “When you see a 13-year-old from the 18th century doing the kind of doodles that kids are doing today, it is so...

Four people are traveling in the dark when they arrive at a river. The narrow bridge can accommodate only two people at a time, and the group has only one torch, which must accompany each party that makes a crossing. Persons A, B, C, and D can cross in 1, 2, 5, and 8 minutes, respectively, and any pair of travelers can move only...

The least knotted of all knots is a simple closed loop, the “unknot.” Certainly this is easy to spot on its own, but adding even a few twists can make it hard to recognize: An elaborately draped loop can be quite difficult to distinguish from a knottier knot. Is this an unknot? (Yes, it is.) Surprisingly, while research is ongoing, it remains unknown whether...

In the 18th century Leonhard Euler famously addressed the question whether it was possible to walk through the city of Königsberg and return to one’s home having crossed each of seven bridges exactly once. The answer, briefly, was no, but in 2013 network scientist Thilo Gross noticed that the city of Bristol has a similar layout, and here the task is possible: If you’re...

Rinaldo Carnielo’s sculpture Tenax Vitae stands in the Galleria Rinaldo Carnielo in Florence. After meeting the sculptor in 1893, Helen Zimmern observed that “for him, the shadow of death pervades all existence,” but “he cares not one jot whether his statues find purchasers so long as he himself is satisfied with the results.”

A paradox by Columbia University logician Haim Gaifman: line 1: The sentence on line 1 is not true. line 2: The sentence on line 1 is not true. line 3: The sentence on line 2 is not true. line 4: The sentence on line 3 is not true. line n + 1: The sentence on line n is not true. All these sentence are...

In the middle of winter when fogs and rains most abound they have a great festival which they call Exmas and for fifty days they prepare for it in the fashion I shall describe. First of all, every citizen is obliged to send to each of his friends and relations a square piece of hard paper stamped with a picture, which in their speech...