On the morning of Aug. 6, 1945, a customer was sitting on the steps of Sumitomo Bank in Hiroshima, waiting for the branch to open, when an atomic bomb exploded over the city. The bank was only 260 meters from ground zero, and as the intense heat burned its stone face white, the customer’s body shielded one section of the steps, leaving a “shadow” in that place.

The steps are now preserved in the Hiroshima Peace Memorial Museum.

In 1946, the British mission to Hiroshima and Nagasaki noted that the surfaces of asphalt roads “retained the ‘shadows’ of those who had walked there at the instant of the explosion.” It called them “objects of macabre interest and pilgrimage for visitors.”

Hansel and Gretl have discovered a gingerbread cottage and are wondering whether to eat some of the tiles on its walls. A witch appears and tells them how they must go about it. “Each of you is to name a whole number between 0 and 100. Hansel’s must be odd and Gretl’s even. No conferring. Whoever chooses the lower number can eat twice that number of gingerbread tiles. Whoever chooses the higher number can eat the lower number.” So, for example, if Hansel chooses 57 and Gretl chooses 30, Hansel will get 30 tiles and Gretl will get 60.

This sounds fine, but the children have just had lessons in game theory and regard this as a non-cooperative game between rational utility maximizers. Gretl knows that Hansel will not choose 99, because 97 would leave him better off if she chose 98 and no worse off if she chose any other number. By the same reasoning, she will avoid 98 and choose 96. In her mind she can follow this train all the way to its end: Rationally, it seems, she must choose 2. Hansel, following it also, finds himself indifferent between 3 and 1. In the end he will receive a paltry two tiles and Gretl either one or four.

Is all of this sound? Gretl says, “There is something radically peculiar about trains of thought which proceed in the subjunctive. You are to work out what you would be rational to do, if I were to choose a number which I shall not choose. I am to do likewise, with each train of thought reproduced inside the other. What happens if either player derails a train by choosing in defiance of it? In that case it becomes radically unclear whether either player still has a rational choice.”

(Martin Hollis, “The Gingerbread Game,” Analysis 54:4 [October 1994], 196-200.)

Whenever I have occasion to classify the persons I meet into three classes, ‘good, medium, and bad,’ I use a needle mounted as a pricker, wherewith to prick holes, unseen, in a piece of paper. … I used this plan for my beauty data, classifying the girls I passed in streets or elsewhere as attractive, indifferent, or repellent. … I found London to rank highest for beauty; Aberdeen lowest.

In 2008, psychologists Viren Swami and Eliana Hernandez set out to compile a beauty map of their own, this time focusing on London. They asked 461 residents to rate the physical attractiveness of men and women in the city’s 33 boroughs. For the record, the City of London, the City of Westminster, and Kensington and Chelsea were rated highest — which correlates with the affluence but not the health (life expectancy) of the residents in those boroughs.

In a mathematical contest, three problems, A, B, C were posed. Among the participants there were 25 students who solved at least one problem each. Of all the contestants who did not solve problem A, the number who solved B was twice the number who solved C. The number of students who solved only problem A was one more than the number of students who solved A and at least one other problem. Of all students who solved just one problem, half did not solve problem A. How many students solved only problem B?

That August, she, Philip Cohen, and Murray Pearce extended the list:

FEED = IRONED
AGED = SILVERED
SIC = SULFURIC
SNED = TINED
SNY = TINY
SOUS = SULFUROUS
SET = SULFURET
SING = SULFURING
SIZING = SULFURIZING
CUED = COPPERED

Likewise, BASIS yields BASILICONS, NAZI yields NEONAZI (and then NEONEONEONAZI, and so on forever), and RES can yield either RHENIUMS or RESULFUR.

07/09/2026 UPDATE: A number of readers point out that NAZI doesn’t work, as the symbol for neon is Ne. But JAR = JARGON! (Thanks Paul.)

Choose a number on this clock face and, starting from 12, spell out that number’s English name as you advance clockwise around the face, one letter per numeral. For example, if you’ve chosen 3, count out T-H-R-E-E and you’ll land on the numeral 5. Adopt this new position as your next chosen number and proceed as before (in this case, counting F-I-V-E and landing on 9). After three or more moves you’ll reliably land on 1.

This works because of a characteristic of Markov chains first observed by Russian mathematician Evgenii Borisovich Dynkin. Here’s a card trick that exploits the same principle.

This recording presents four pairs of tones, each pair separated by three whole tones, or half an octave. Curiously, some listeners hear the interval as ascending, others as descending. (In fact the tones used are ambiguous as to octave, so there’s no objectively right answer.)

Even more curiously, sometimes a listener’s perception reverses when an interval is transposed, say from C-F# to G#-D, even though nothing else has changed.

Diana Deutsch discovered the effect in 1986.

Age, if healthy, happy
Ancestors, their examples should excite to great and virtuous actions
Animals, a degree of gratitude owing to them that serve us
Atheist, behaviour of one in sickness
Barbers, inconveniences attending their being historians
Classics, absolutely necessary to study them
Climate, British, very inconstant
Cowards never forgive
Cunning opposed to wisdom
Duels, the danger of dying in one, represented
Earth, its inhabitants ranged under two general heads
Examination, self, advantages attending it
Fame, common, house of, described
Feet, pretty ones, a letter concerning them
Flies and free-thinkers compared
Gardens, the best not so fine as nature
Honour, temple of, can be entered only through that of Virtue
Horse, described by Homer, Virgil, Oppian, Lucan, and Pope
Janglings, matrimonial
Ladies, all women such
Laughter, the chorus of conversation
Master, how he should behave to his servants
Pedants, their veneration for Greek and Latin condemned
Peruke, a kind of index to the mind
Possession, true, consists in enjoyment
Reproof distinguished from reproach
Sloth more invincible than vice
Terrible Club, account of it
Time not to be squandered
Wisdom opposed to cunning
Women should have learning

Henry Wheatley said that the indexes “possess that admirable quality of making the consulter wish to read the book itself.” Leigh Hunt wrote, “As there is ‘a soul of goodness in things evil’ so there is a soul of humor in things dry … so an Index, like the Tatler’s, often gives us a taste of the quintessence of his humor.”

From Henry Dudeney:

“The illustration represents a map (considerably simplified for our purpose) of a certain district on the Continent. The circles are towns and the lines roads. During the war five regiments marched to new positions on the same night. The body stationed at the upper A marched to the lower A, that at the upper B to the lower B, that at the upper C to the lower C, that at the upper D to the lower D, and the regiment at the left-hand E marched to the right-hand E. Yet no regiment ever saw anything of any other regiment. Can you mark out the route taken by each so that no two regiments ever go along the same road anywhere?”