In 1939, a cartographer who was not really a cryptographer wrote an introductory book on codes for Oxford University Press, placed a challenge cipher on its final page, invited readers to test their skill on it, and then forgot how he had made it.
Alexander D'Agapeyeff's 395-digit puzzle appeared in exactly one edition of Codes and Ciphers before being quietly removed. His son later recalled his father being "extremely embarrassed" about the whole affair. More than 86 years later, nobody has managed to solve it either, making the D'Agapeyeff Cipher the only famous unsolved cipher in cryptographic history whose creator couldn't crack it himself.
Background: The Wrong Man for the Job
Alexander D'Agapeyeff was Russian-born but had settled in Britain young, building a career as a cartographer rather than a cryptanalyst. When his publishers at Oxford University Press decided in the late 1930s that a popular book on codes and ciphers might sell well given the growing prospect of European war, they approached D'Agapeyeff on the strength of his reputation as a capable general writer, not as a specialist in the field. He accepted, spent time researching historical cipher methods, and produced a clear, readable survey of classical cryptography, complete with worked examples, that was published in 1939, the same year Britain entered the Second World War.
The book sold well enough to run to multiple editions. At the end of its first and only first-edition run, on page 144, D'Agapeyeff added a single paragraph: "Here is a cryptogram upon which the reader is invited to test his skill." Below it sat 395 digits, arranged in groups of five. No key was provided. No method was hinted at. When readers and other cryptographers began writing to ask for the solution, D'Agapeyeff's response, confirmed by his son in later years, was that he had simply forgotten the method and key he had used to construct it. The cipher was omitted from the 1942 second edition and every subsequent reprint, though not before it had entered the small, persistent canon of famous unsolved puzzles that cryptographers periodically return to.
What the Numbers Actually Tell Analysts
Statistical analysis of the D'Agapeyeff cipher has produced a relatively consistent picture of its likely structure, even if that structure has not yet yielded a readable message. When the 395 digits are read as 196 two-digit pairs, with three trailing zeros treated as nulls, the index of coincidence for those pairs sits at approximately 1.812, significantly higher than the value expected from random digit sequences and consistent with an underlying English plaintext that has undergone a substitution cipher. This statistical fingerprint strongly suggests the cipher is built on a Polybius square, a classical 5×5 grid technique in which each letter of the alphabet is encoded as the coordinates of its row and column, producing exactly the kind of two-digit numerical pairs the ciphertext displays.
D'Agapeyeff's own book illustrates the Polybius square method explicitly, walking readers through a worked example of precisely this approach on pages 140 through 143, making it almost certain that a Polybius square forms at least the first layer of the cipher's construction. The complication is the second layer: the flat, non-random pattern of digit-pair frequencies across the full ciphertext suggests that a transposition step, in which the encoded output is rearranged according to a separate key, was applied after the initial substitution, compounding the difficulty well beyond a simple Polybius decode. A dedicated computational research project, dagapeyeffresearch.com, has modeled the cipher as a 14×14 transposition grid applied over a Polybius-encoded message, running systematic brute-force tests across candidate key combinations, without yet producing a confirmed plaintext.
| Feature | Detail |
|---|---|
| First published | 1939, in Codes and Ciphers (Oxford University Press, 1st ed.) |
| Author | Alexander D'Agapeyeff (1891–1969), cartographer |
| Total digits | 395 (80 groups of five; three trailing zeros treated as nulls) |
| Effective pairs | 196 two-digit pairs after null removal |
| Likely first layer | Polybius square substitution (described and exemplified in the same book) |
| Likely second layer | Columnar transposition (statistical evidence; not confirmed) |
| Removed from later editions | Yes, from the 1942 second edition onward |
| Status | Unsolved; creator admitted forgetting the method before his death in 1969 |
The Embarrassment Problem and the Encryption Error Theory
The most humanly specific detail in the D'Agapeyeff case is the one that makes it unlike any other cipher in this series: the author's admission that he had forgotten his own method. D'Agapeyeff died in 1969, having never published a correction, a key, or a solution, and having never, as far as the historical record shows, offered any further help to the researchers who periodically contacted him. His son's description of him as "extremely embarrassed" about the affair is the closest thing to first-person testimony that survives, and it carries a slightly different implication than simple forgetfulness: embarrassment suggests D'Agapeyeff recognized he had set a puzzle he could no longer justify having set.
This opens a second, related possibility that has attracted cryptanalysts since at least the 1970s: that D'Agapeyeff did not merely forget the key but made an actual encryption error during construction, producing a ciphertext that does not correspond to any cleanly recoverable plaintext even if the method and key were known. A professional cryptographer constructing a challenge cipher would typically verify it by decrypting their own output before publication. D'Agapeyeff, who was not a professional cryptographer, may simply have built the layers in a way that introduced an uncorrectable error, which would simultaneously explain why he forgot the method, why he never provided the solution, and why every systematic computational attack to date has produced only fragments and near-misses rather than a clean decode.
Theories and Explanations
Three positions dominate current thinking among researchers who work on the cipher. The most optimistic holds that D'Agapeyeff constructed a genuine, error-free Polybius square plus transposition cipher, forgot the specific key phrase he used to generate his 5×5 grid, and that the puzzle is solvable given sufficient computational power and the right key-search strategy. This position is supported by the statistical properties of the ciphertext, which are consistent with real encoded English, and by the fact that a dedicated brute-force research project has been systematically narrowing the candidate space without conclusively eliminating the possibility of a correct solution.
The second, more pessimistic position holds that D'Agapeyeff made an encryption error during construction, introducing a corruption that makes the ciphertext effectively unsolvable by any standard method, regardless of the key. This would explain the absence of clean solutions in over eight decades of attempts and the cipher's own creator's inability to reconstruct his steps. The third, minority position treats the entire cipher as filler without a genuine underlying message, a placeholder puzzle that D'Agapeyeff assembled from numerical patterns without encoding actual plaintext. The statistical evidence against this view is fairly strong, since the index of coincidence argues for real linguistic content, but it has not been conclusively ruled out.
The Curious Connection
The D'Agapeyeff Cipher closes this series at the most deflating possible point: not with a villain's taunt, a forger's trick, or a buried treasure, but with a cartographer's embarrassment. Every other cipher in this series was built by someone who knew exactly what they were doing: Zodiac's homophonic transposition was calculated, Kryptos's K4 was deliberately hardened, Beale's authors, if they existed, designed their numbers to sustain long-term interest, and Elgar's semicircles were drawn by someone who had already broken another cipher for sport. D'Agapeyeff's puzzle may be the only famous unsolved cipher in history that was created not through malice, artistry, or commercial intent, but through a writer out of his depth making a mistake he was too embarrassed to admit in print and too forgetful to reconstruct.
This matters for how the series as a whole should be read. The D'Agapeyeff Cipher is a reminder that not every unsolved mystery involves a secret being deliberately withheld: sometimes the person who appears to be hiding something simply lost it. The difference between a hidden truth and a forgotten one can look identical from the outside for eighty-six years and counting, and the statistical footprint of a genuine encoded message provides no information about whether the person who encoded it still knows what it says. Mystery, as this series has repeatedly found, is not always the product of intention. Sometimes it is the product of ordinary human fallibility, and the gap between those two kinds of mystery is considerably harder to close.
FAQ
What is the D'Agapeyeff Cipher?
The D'Agapeyeff Cipher is a 395-digit numerical puzzle published on the final page of Alexander D'Agapeyeff's 1939 book Codes and Ciphers, presented as a reader challenge. It was removed from all later editions after D'Agapeyeff admitted he had forgotten the method and key he used to construct it.
Who was Alexander D'Agapeyeff?
Alexander D'Agapeyeff (1891–1969) was a Russian-born British cartographer, not a professional cryptographer. He was commissioned by Oxford University Press to write an introductory book on codes and ciphers based on his general writing reputation rather than cryptographic expertise.
Has the D'Agapeyeff Cipher ever been solved?
No confirmed solution exists. Statistical analysis strongly suggests the cipher is built on a Polybius square substitution combined with a transposition step, but no researcher has produced a complete, coherent plaintext from the ciphertext in over 86 years of attempts.
Why did D'Agapeyeff remove the cipher from later editions?
D'Agapeyeff admitted he had forgotten the method and key he used to create it. His son later described him as "extremely embarrassed" about the situation. The cipher was quietly dropped from the 1942 second edition and all subsequent reprints without explanation.
Could D'Agapeyeff have made an encryption error that makes the cipher unsolvable?
Many researchers consider this the most plausible explanation. Because D'Agapeyeff was not a professional cryptographer and appears not to have verified his cipher by decrypting it before publication, he may have introduced an uncorrectable error during construction, which would simultaneously explain his forgetfulness and the failure of every systematic decryption attempt to date.