Srinivasa Ramanujan devised this magic square to mark his own birthday. He began with a Latin square (upper right) in which the numbers 1, 2, 3, and 4 appear in each row, column, and long diagonal as well as in the four corners, the four central squares, the middle squares in the top and bottom rows, and the middle squares in the outermost columns. Note the adjustments that would be necessary to reduce the four top cells to zero, and arrange these adjustments in the diagonally reflected pattern shown in the upper left. Now adding these two squares together produces the square in the lower left, which gives us a formula for creating a magic square based on any date (in the format 1 January 2001). The example at lower right is based on Ramanujan’s own birthday, 22 December 1887 (so D = day = 22, M = month = 12, C = century = 18, and Y = year = 87). In this example all 16 numbers are distinct, but that won’t be the case with every date.

# Science & Math

# The Mozart Café Problem

You and a friend agree to meet on New Year’s Day at the Mozart Café in Vienna. You fly separately to the city but are dismayed to learn that it contains multiple cafés by that name.

What now? On the first day each of you picks a café at random, but unfortunately you choose different locations. On the second day you could both go out searching cafés, but you might succeed only in “chasing each other’s tails.” On the other hand, if you both stay where you are, you’ll certainly never meet. What is your best course, assuming that you can’t communicate and that you must adopt the same strategy (with independent randomization)?

This distressingly familiar problem remains largely unsolved. If there are 2 cafés then the best course is to choose randomly between them each day. If there are 3 cafés, then it’s best to alternate between searching and staying put (guided by certain specified probabilities). But in cases of 4 or more cafés, the best strategy is unknown.

In 2007 a reader wrote to the *Guardian*, “I lost my wife in the crowd at Glastonbury. What is the best strategy for finding her?” Another replied, “Start talking to an attractive woman. Your wife will reappear almost immediately.”

# Prolific

Staggering fact: Science historian Clifford Truesdell estimates that “[a]pproximately one-third of the entire corpus of research on mathematics and mathematical physics and engineering mechanics published in the last three-quarters of the eighteenth century” was written by a single person, Leonhard Euler.

The work of compiling Euler’s scientific writings has been going on since 1908 and will fill 81 volumes when complete. Mathematician William Dunham writes, “A typical volume of the *Opera Omnia* is large, running from 400 to 500 pages — although some contain over 700. In size and weight, such a volume resembles its counterpart from (say) the *Encyclopedia Britannica*. No one short of an athlete could carry more than five or six at once, and to cart off the entire collection — over 25,000 pages in all – would require a forklift.”

Laplace wrote, “Read Euler, read Euler, he is the master of us all.”

# Prince Rupert’s Cube

In the 17th century, Prince Rupert of the Rhine wondered whether one cube might pass through another of the same size. John Wallis showed that the answer is yes, and, perversely, Pieter Nieuwland showed a century later that one cube can even accept another *larger than itself* — fully 6 percent larger in the optimal case. The diagram above shows the dimensions (blue) of a square tunnel through a unit cube that will accommodate a second unit cube (green) with room to spare.

Remarkably, all five Platonic solids have the “Rupert property” — a regular tetrahedron, for example, will fit through an identical tetrahedron if the hole is contrived cleverly enough. Whether every convex polyhedron can perform this unlikely feat is an open question.

# Ordnance

# Inside Out

The Pythagorean theorem has a reciprocal variant:

In combination with the inverse-square law, this means that identical lamps placed at A and B will produce the same light intensity at C as a single lamp at D.

# Misc

- It’s illegal to enter the Houses of Parliament wearing a suit of armor, according to a 1313 statute.
- “All things in moderation” is an immoderate policy.
- If a prime number is made up entirely of 1s (e.g., 11), then the number of its digits is prime.
- The word CARBON is itself made up of element symbols (Ca, Rb, O, N). (Dmitri Borgmann)
- Interior decorator Nicholas Haslam: “All it comes down to is making a setting in which people look prettier.”

07/17/2024 UPDATE: Several readers point out, correctly, that carbon is hardly the only elemental “chemical word” — indeed, some elements can be spelled in multiple ways. I’ve assembled this list from multiple contributions:

ArSeNiC ArSeNIC

AsTaTiNe

BiSmUTh BISmUTh

CArBON CaRbON

CoPPEr COPPEr

IrON

KrYPtON

NeON

OGaNeSSON OGaNEsSON

PHoSPHoRuS PHOSPHoRuS PHOsPHoRuS PHoSPHORus PHOSPHORuS PHOsPHORuS

SiLiCoN SiLiCON SILiCON SILiCoN

SiLvEr SILvEr

TeNNeSSINe TeNNEsSiNe TeNNEsSINe

TiN

XeNON XeNoN

TiN is even a valid compound, titanium nitride.

Of these Borgmann had found arsenic, carbon, iron, neon, phosphorus, silicon, and xenon when he wrote in 1974, “surely the most unusual is CARBON which can be factored into elements not including itself.” But that property wasn’t unique even within his limited list, as can be seen above.

Many thanks to readers Gareth McCaughan, Catalin Voinescu, and Eric Harshbarger for writing in about this.

# Unusual Biological Names

- Herpetologist Mark Scherz named three tiny species of Malagasy frog
*Mini ature*,*Mini scule*, and*Mini mum*. - Malacologist Alan Solem named a Fijian land snail
*Ba humbugi*. - The name of each species in the African spider genus
*Palindroma*is a palindrome:*P. aleykyela*,*P. avonova*,*P. morogorom*,*P. obmoimiombo*,*P. sinis*. - The binomial name of the crowned slaty flycatcher has 15 syllables:
*Griseotyrannus aurantioatrocristatus*. - Malacologist John Stanisic named an Australian land snail
*Crikey steveirwini*. - The Australian leafhopper genus
*Dziwneono*, named by entomologist Irena Dworakowska, is Polish for “It is strange.”

In 1977, on receiving a package of insect specimens from a colleague, entomologist Arnold Menke exclaimed, “Aha, a new genus!” His colleague Eric Grissell responded “Ha” doubtfully. Menke was proven right and named the species, an Australian wasp, *Aha ha*. He ordered a custom registration plate for his car bearing the same phrase. Further odd names.

# The Earth-Moon Problem

Suppose that each country on Earth has a colony on the moon and that we want to draw maps on which each nation’s territory receives a consistent color. How many colors would we need?

In 1980 Thom Sulanke showed that we might need as many as nine (above), but it’s possible that a particularly challenging map would require more than that. The problem remains unsolved.

# Return Engagement

On Easter Saturday 1921, pharmacologist Otto Loewi dreamed of an experiment that would prove that the transmission of nerve impulses was chemical rather than electrical. He scribbled down the idea and went back to sleep, then discovered the next morning that he couldn’t read the note.

That day, he said, was the longest of his life. Fortunately, the dream returned to him that night, and this time he went immediately to the laboratory. Thirteen years later he received the Nobel Prize for discovering the role of acetylcholine as an endogenous neurotransmitter.