Problem We gave Claude Fable 5.1 an open task: solve Sir Thomas Urquhart’s Cyphral Distich. It appears to have actually solved it, and the solution is quite embarrassing for humans in hindsight. At the end of Urquhart’s Logopandecteision is a cryptogram consisting of two lines of 32 numbers each, called the Cyphral Distich.

A cryptogram is a short message deliberately encoded so it can’t be read without knowing the rule that produced it. Here the entire puzzle input is these 64 numbers, and the goal is to recover the hidden plaintext:5.3.27.38.32.14.21.8.66.8.70.39.5.9.12.18.2.3.56.5.1.7.3.2.13.19.3.25.9.3.16.6.25.15.13.6.11.20.5.1.2.12.1.20.20.49.20.20.35.33.4.6.8.35.5.33.5.5.18.10.3.11.32.42. This cipher has remained seemingly unsolved for centuries.

It was posed as an open problem in Notes and Queries in 1899, appeared again in 20th-century cryptography literature, and was later listed by historical-cipher researcher Klaus Schmeh among his Top 50 unsolved encrypted messages. Various people attempted to decipher it, but it seems they were missing one crucial hint. They tried methods like frequency analysis, substitution, and homophonic substitution, and none of these approaches worked.

That’s because they missed one easy clue. Solution After 44 minutes, 176k tokens, and zero interjections from me, Fable 5.1 arrived at a solution. It tried a few approaches, but was finally able to solve it with two central realizations.

First: the cryptogram is printed immediately after Urquhart’s 32 Proquiritations, and Urquhart even goes out of his way to emphasize that number. I know, surprising. He says: "there can no number like that of two and thirty … be pitched upon"Second: the poem accompanying the cipher promises that an honest reader will find in it "his own heart’s wishes, and the Author’s minde." The Proquiritations themselves repeatedly conclude with formulations like "is the desire," "wish," or "hope of."If you put these clues together:32 Proquiritations. 32 numbers in the first cipher line. 32 numbers in the second. "Wishes."Most historical attempts assumed the key was external: a cipher alphabet, or some mapping of numbers to letters or words, that had to be reconstructed from outside the text.

But the key was not an external cipher alphabet at all. The key was the book itself. The rule was simple: for the i-th number in a cipher line, go to the i-th Proquiritation, use that number as a word index, and take the first letter of that word.

With this, you get: O GOD UPHOLD KING CHARLS THE SECOND ANDMAKE HIM THE SUPREME RULER OF THIS LANDAnd the result is extremely self-verifying. Each line contains exactly 32 letters and ends and / land (a rhyming 2 line verse), consistent with the promised distich. It also makes historical sense: Urquhart was a committed Royalist.

Hiding a prayer for Charles II in the text is entirely consistent with his politics. Urquhart left a second, much larger cryptogram in the same style — the Cyphral Octastich in The Jewel (1652), 285 numbers instead of 64, and just as unsolved. From this, Fable 5.1 was also able to decipher it: Result: the Cyfral Octastick is solved (all but nine letters)Rule.

The Jewel (1652) has exactly 284 numbered pages, and the octastick + decagram contain 285 numbers. The k-th number (counting straight through the eight lines and the Decagram) is a word index into page k of the book; take the word's first letter. Same idea as the Distich (number i → Proquiritation i), with pages instead of paragraphs — and, as in the Distich, Urquhart almost always picked the first word on the page starting with the letter he needed (231 of 275 readable positions are exact first-occurrence hits in the EEBO-TCP text; the other 44 are 1–3 words off for identifiable transcription reasons — hyphenated words at page tops, hyphenated compounds, "&", paragraph numbers, an untranscribed Greek phrase).

Plaintext (ottava rima, — a royalist prayer written in London, March 1652): GREAT LORD, MANTAINE THAT REGAL...