A chestnut from physics:
Two cannons are aimed directly at one another. One is on the floor of a valley, and the other is on a promontory. Neglecting air resistance, if the two fire simultaneously, what will happen?
Wildlife
Just before retiring in 2011, Swiss cartographer Paul Ehrlich hid a drawing of a marmot in a map of the Aletsch Glacier.
Hidden drawings are something of a tradition in Swiss maps.
64 Coins
A puzzle from the site Riddle of the Day:
A warden offers a challenge to two prisoners. The first prisoner will enter a room that contains a chessboard. On each of the board’s 64 squares is a coin that’s either heads up or tails up. The guard will identify one square as the “target.”
The first prisoner must turn over exactly one coin and then leave the room. The second prisoner must then enter and, solely by viewing the board, determine which square is the target.
If they succeed, both prisoners will go free. They can confer beforehand on a strategy, but they may not communicate after that. Can they establish a plan that will always work?
Singmaster’s Conjecture
In Pascal’s triangle, each number is the sum of the two above it. Obviously, the infinite pyramid contains an infinite number of 1s, but most numbers appear surprisingly seldom:
- 2 appears just once.
- 3, 4, 5, and all odd primes appear exactly twice.
- 6 appears three times.
- Infinitely many numbers appear exactly six times, but we don’t know whether any appear exactly five or seven times.
- 3003 appears eight times, possibly the only such specimen.
In 1971, Berkeley mathematician David Singmaster suggested that there may be a finite upper bound on the number of times that any number can appear (apart from 1). But that remains an unsolved problem.
The Rilke Cryptogram
In one copy of a 1942 edition of German historian Gert Buchheit’s biography of Rainer Maria Rilke, someone has glued a typewritten and hectographed alphanumeric text. The text fills 33 pages with 18,760 characters in groups of four. Analysis shows that it’s less ordered than English or German but more ordered than random text. To date, no one has been able to make sense of it.
Here’s the cryptogram itself, and here’s an analysis.
From Klaus Schmeh’s Encrypted Book List.
06/21/2026 UPDATE: Reader Logan Swiecki-Taylor writes:
I have a note on the aforementioned post.
The cryptography community (including the author of that very blog, Klaus Schmeh, security expert Tobias Schrödel, and statistician Floe Foxon) essentially ‘solved’ the mystery by figuring out exactly what it is: It is literally ‘Keyboard Mashing.’
The text was generated by someone mindlessly sliding their fingers across a German QWERTZ typewriter.
- Groups like
qwer,tzui, andcvbnare just straight lines across the keys.- Groups like
cxswandmju7are diagonal swipes.- Statistical analysis published in the journal Cryptologia in 2022 mathematically proved that the physical distances between the keys pressed are too short to be random or to be any known substitution cipher. It is intentional ‘lazy typing.’
The pages in the book were printed using a ‘hectograph’ (an early duplication method used for making a few dozen copies of a document). The prevailing consensus among historians is that this was practice material for radio operators learning Morse Code.
Military radio operators needed to practice transmitting and receiving meaningless letter sequences because actual encrypted military communications (like Enigma messages) look like random 4-letter or 5-letter blocks. Instead of going through the tedious mathematical effort of properly encrypting a real message just for a training exercise, an instructor simply rolled their fingers across a typewriter to generate pages of fake ‘ciphertext’ and printed copies for the class to practice their Morse transmissions.
Timeline of crypto community decipher
January 2018: The Initial Clue (Crowdsourcing)
The mystery was first brought to public attention in early 2018 when the book’s owner, Dr. Karsten Hansky, shared the pages with German crypto-historian Klaus Schmeh. Schmeh posted it on his popular cryptography blog on January 10, 2018, listing it as an ‘unsolved World War II cryptogram.’
On that exact same day, an astute blog commenter going by the name ‘Gerd’ pointed out that military Morse code training typically used random gibberish so that students couldn’t simply ‘guess’ words if they missed a letter. He suggested that it was just a practice text.
2020: The ‘Keyboard Mashing’ Realization
Over the next couple of years, Schmeh, alongside German IT security expert Tobias Schrödel and other blog readers, looked closer at the letter groupings. They noticed the high frequency of spatial sequences (like
qwerandaswq) and realized the text wasn’t randomly generated with dice or cryptography, but by someone simply rolling their fingers around a German QWERTZ typewriter. Schmeh eventually published an update officially re-classifying the mystery as ‘probably solved’ and removing it from his list of unsolved ciphers.August 2022: The Mathematical Proof
The final nail in the coffin came from academia. In August 2022, a data scientist and statistician named Floe Foxon published a peer-reviewed paper titled ‘A treatise on the Rilke cryptogram’ in the journal Cryptologia.
Foxon mapped the letters of the cryptogram to a standard 1940s German typewriter layout. Using statistical analysis, Foxon mathematically proved that the physical distances between the consecutive keystrokes were drastically shorter than what would occur in natural language, a known substitution cipher, or true randomness.
Thanks, Logan. The solution is even more interesting than the puzzle!
Progress
I’d missed this: In 2006 a geneticist, a philosopher, and a chicken farmer all agreed that the egg came before the chicken.
Nottingham University geneticist John Brookfield pointed out that the first chicken (the first creature bearing chicken DNA) must have begun as an embryo in an egg. “The first living thing which we could say unequivocally was a member of the species would be this first egg, so I would conclude that the egg came first.”
David Papineau, philosopher of science at King’s College, London, agreed. “I would argue it is a chicken egg if it has a chicken in it. … If a kangaroo laid an egg from which an ostrich hatched, that would surely be an ostrich egg, not a kangaroo egg.”
And Charles Bournes, chair of trade body Great British Chicken, said, “Eggs were around long before the first chicken arrived. Of course they may not have been chicken eggs as we see them today, but they were eggs.”
According to the BBC, “Professor Brooke added the debate could finally be laid to rest.”
In a Word
ladrone
n. a thief; robber; highwayman; rogue
depeculation
n. a robbing or embezzling
desponsate
adj. married
adhorn
v. to make a cuckold of
According to legend, French highwayman Claude Duval agreed not to rob one gentleman if his wife would dance the courante with him by the wayside.
He was hanged at Tyburn in 1670 “to the great grief of the women.” A memorial in Covent Garden reads, “Here lies DuVall: Reder, if male thou art, Look to thy purse; if female, to thy heart.”
Reckoning
A problem from the October 1961 issue of Eureka, the journal of the Cambridge University Mathematical Society:
When A was three times as old as B was the year before A was a half of B’s present age, B was 3 years younger than A was when B was two thirds of A’s present age. A’s and B’s ages now total 73. How old are A and B?
A Salt Hygrometer
An “easy and curious method of foretelling rainy or fine weather,” from an 1860 book on conjuring, of all places:
“[T]he best instrument of all, is a good pair of scales, in one of which let there be a brass weight of a pound, and in the other a pound of salt, or of saltpetre, well dried; a stand being placed under the scale, so as to hinder it falling too low. When it is inclined to rain, the salt will swell, and sink the scale: when the weather is growing fair, the brass weight will regain its ascendancy.”
Black and White
A puzzle in chess logic from The Batsford Chess Puzzle Book. Who made the last move, and what was it? (There’s no trick — everything is just as it seems.)