The book's toolkit · D'Agapeyeff

pp. 16–17 · Chapter I

Polybius' torch code — the ancestor of the whole thing

Five groups of five letters, Q dropped to get exactly 25. The signaller holds ten torches; the right hand gives the group number, the left hand the letter within it. Two torches right and four left is the fourth letter of group two.

Bearing: this is the challenge cipher's skeleton, stated in the book's first chapter. Row coordinate, then column coordinate, one symbol per plaintext letter. The only thing d'Agapeyeff changed was what the coordinates are written with.

p. 117 · Chapter VI

The keyword square and the key numbering

Keyword MANCHESTER, repeated letters struck out to give MANCHESTR, then numbered by alphabetical rank: 5 1 6 2 4 3 8 9 7. The remaining letters of the alphabet fill the square, and the cipher alphabet is read down the columns in numerical order.

Bearing: the exact mechanism for turning a word into a column order. The Workbench's transposition tool implements this numbering, so you can type a keyword rather than a permutation.

pp. 117–118 · Chapter VI

Groups of five, and nulls to fill them

"For transmission, the cipher is sent in groups of five letters… ('Z' here is a 'null' to complete the five letters)."Codes and Ciphers, p. 117

Bearing: this is why the challenge ends 92000. Two real digits and three nulls to round out the final group — which is what leaves 392 working digits and 196 units. Not a guess: the book states the convention three separate times.

p. 118 · Chapter VI

The A–E square — the same cipher in letters

A 5 × 5 grid with the keyword written in first and the rest of the alphabet after it, J omitted "so as to get correct square". Rows and columns are labelled A to E, and ENEMY ATTACKS becomes BA AC BA AA ED AB BC BC AB AD CE BB, transmitted as BAACB AAAED ABBCB CABAD CEBBE EEEEE.

Bearing: the closest thing in the book to the challenge. Identical structure — one plaintext letter, one coordinate pair, five-letter transmission groups, nulls at the end. Note especially that the square is keyword-filled, not alphabetical, and that one letter is dropped to make 25 fit.

pp. 122–124 · Chapter VI

Playfair, with keyword CLIQUE

Twenty-five subdivisions, I and J treated as one letter, text split into pairs, doubled letters broken by a dummy X or Z.

Bearing: ruled out as the challenge's method — Playfair is letter-to-letter and cannot produce 18 symbols over 196 units — but it confirms which 25-letter reduction d'Agapeyeff reached for by habit: I and J merged. Worth preferring in the square editor.

pp. 124–125 · Chapter VI

Combined Substitution–Transposition — the obvious suspect

Three operations. First, ADVANCE BRIGADE TOMORROW through a MANCHESTER square into A–E pairs. Second, the resulting stream of single letters written across a keyed rectangle and read down the columns. Third, re-pair that transposed stream and look each pair up again, giving EOLTQ AEBMR NDTPF CSLXH SCZZZ for transmission.

Bearing: everyone's first hypothesis, and the measurements kill it. Step two fractionates — it separates the two halves of each coordinate pair before shuffling them. Run on this message it would leave no trace of the 6–9 / 1–5 alternation, and the alternation is perfect (E4). The narrow-width version that would survive E4 was then enumerated to exhaustion — all 641,000 alternation-preserving keys at widths 3 to 13 — and rejected. So was the version with the transposition moved up a level, shuffling whole units. See Section 4.

p. 127 · Chapter VI, section 3

"Numeral or Figure Ciphers" — the chapter the challenge belongs to

"In the most simple cases figure ciphers mean only that letters are replaced by numbers. Arbitrarily, the equivalent of A, B, C, D, &c., may stand for any numbers (preferably double) from 10 to 99… The odd pairs of figures may represent either frequently-used syllables… or a complete code of short sentences or personal names."Codes and Ciphers, p. 127

The same page adds that numbers can serve as the keyword — "instead of Manchester as keyword you can simply use the current dates, as for instance 2. 5. 1939, or any other sequence of numbers."

Bearing: the single most important paragraph in the book for this problem. It licenses two-digit letter equivalents and tells you that some pairs may be syllables or whole names instead of letters — the only mechanism in the book that would produce the observed frequency profile (E6). E7 shows it cannot be the whole answer, but it can still sit underneath the transposition. The date suggestion is worth remembering: a 1939 book with a 1939 key, and "2. 5. 1939" is a nine-figure key.

pp. 127–128 · Chapter VI

Selenus's syllable table, and an explicit invitation

A grid of vowel-plus-consonant syllables — AB AH AN AG AM AT / EC EK EG EF EM ES / OF OM OS OC OK OG / UN UB UT UF UP — which d'Agapeyeff criticises for omitting consonant-plus-vowel, then recommends anyway:

"it may serve as a foundation for a syllable cipher which may be quite interesting for the reader to compose."Codes and Ciphers, p. 128

Bearing: thirty-one pages before setting the challenge, in the numeral chapter, the author suggests building a syllable cipher on a small grid. A 20-unit syllabary reproduces the cipher's odd frequency profile far better than any alphabet does — encoding real English through one gives about 19.8 distinct units and 88% in the top thirteen, against the alphabet's 24 and 84%, where the cipher shows 18 and 96%. It cannot be the answer on its own (E7 rules that out for every substitution), but as the layer under a transposition it remains untested.

pp. 129–130 · Chapter VI

Dictionary code, then a second encipherment

Page number plus word number, five digits per word, with leading zeros added "to keep to the uniformity". Then: "These figures, if greater secrecy is required, could again be enciphered… Divide the figures into pairs and then convert them into letters by means of the table given on p. 130." That table is a 10 × 10 grid indexed by first figure and second figure, and it ends NULLS: WA, WE, W, to end message in groups of five letters.

Bearing: proof that d'Agapeyeff thought in two-layer numeric systems and in digit pairs. The direct reading — that the challenge is a dictionary code in five-digit groups — is dead on E1. The inverted reading is not: a numeric layer underneath a coordinate square would give a plaintext with no English letter statistics at all, which is exactly the shape of E6.

pp. 135–136 · Chapter VII

His own opening moves

Decide first whether it is code or cipher. Then decide transposition or substitution — by the proportion of vowels to consonants, since transposition rearranges the original letters and leaves that proportion intact. Then arm yourself with "squared paper, tracing paper, a graduated ruler", counters, and coloured pencils.

Bearing: the vowel test is the one instrument he gives that we cannot use — it needs letters, and we have coordinates. Sections 2 and 3 substitute the modern equivalents: index of coincidence, n-gram scoring against controls, and a null model built from the cipher's own digits.

pp. 141–145 · Chapter VII

The A–E cryptogram he could not immediately read

A friend hands him a message in which "only the first five letters of the alphabet repeat themselves". He splits it into pairs in red pencil, builds a bigram frequency table, finds CE = E and CD DB = TH, and works out from there. Then the warning:

"The letters are seldom put in such a straightforward alphabetical order; both the plain text and the cipher letters (capitals) would be all jumbled together and not put in any obvious order."Codes and Ciphers, p. 142

Bearing: expect the square to be scrambled, and expect the row and column labels themselves to be in no natural order. That is why the square editor lets you edit the labels as well as the cells — and it is why brute force over 25! is not a plan.

pp. 144–146 · Chapter VII

On the encipherer's mistakes

"here I came to the first mistake made by the 'encipherer'. The 'F' of 'of' was omitted… There are two missing letters and one misspelling… It is very common in deciphering to come across mistakes either by the encipherer or by telegraphists, signallers, or others concerned with the transmission of the cipher."Codes and Ciphers, pp. 144–146

Bearing: the author's own testimony that amateur encipherment is error-prone, written fourteen pages before he enciphered something himself and never wrote down how. The stray zero at digit 195 is the visible half of whatever went wrong; there may be more.

pp. 150–153 · Chapter VII

How he says to attack a transposition

Count the letters, factor the count into a rectangle — "there are 36, which is 6 × 6, and we therefore construct a square accordingly" — write the cipher down the columns, then shuffle columns until a line reads. He notes that transposition is harder than substitution because it takes "a great deal of patience and perseverance to plod through dozens of possible combinations".

Bearing: 196 = 14 × 14 is precisely the invitation this method sets up, and it is almost certainly deliberate. The 14 × 14 view in Section 1 and the transposition tool in the Workbench are there to take him up on it.

p. 159 · Chapter VII, last page

The invitation

"Here is a cryptogram upon which the reader is invited to test his skill." Codes and Ciphers, p. 159 — the last sentence before the Bibliography

Bearing: he gives no hint of the method, no key length, no promise of a solution, and — unlike the two exercises earlier in the chapter — no answer at the end. The 1952 reprint drops the paragraph entirely.