Cryptogram

A short sentence encrypted with a simple substitution cipher: one fixed swap for each letter of the alphabet, used consistently from the first word to the last. Every A in the saying becomes the same symbol, and that symbol never means anything else. The spaces, commas and full stops are untouched — which is the whole reason the puzzle is solvable, because word lengths and word shapes survive the encryption completely.

There is no key hidden anywhere, and no arithmetic. You recover the key the way a codebreaker does: by noticing that a three-letter word appears four times, that one symbol turns up more than any other, that a particular word has its first and last letter the same. Each deduction constrains the next, and a wrong one starts producing impossible spellings within a word or two. The full method is on how to solve cryptograms.

Because a key with a letter left in place is a free gift and a lie at the same time. It hands the solver a letter the moment they spot it, and it quietly breaks the reasoning everyone uses: you decide the commonest symbol is probably E, you try it, and it turns out E was written as E all along — you have learned nothing about the rest of the key. So the key here is always a derangement, a permutation with no fixed point, which is the same convention printed cryptograms have used for a century.

The cost is smaller than it sounds. Of the 403,291,461,126,605,635,584,000,000 ways to permute 26 letters, 148,362,637,348,470,135,821,287,825 have no letter in its own place — 36.79%, which is 1/e to four figures. So barring one letter from itself still leaves roughly 1.48 × 10²⁶ keys. Far more than this site can ever reach, in fact: a puzzle number here is a 32-bit integer, so there are a few billion distinct puzzles rather than 10²⁶ of them, and two puzzle numbers occasionally land on the same key. That costs you nothing as a solver, and the guarantee that matters is the other one — the same number always gives you the same puzzle, on any device, forever.

Through the short words, always. English has exactly two one-letter words, A and I, and in this corpus every single one is A — a proverb never says I. A three-letter word is THE far more often than anything else, and once THE is placed you have three of the most common letters in the language working for you everywhere else in the sentence.

Word shape is the other lever, and it survives encryption exactly. SEES and TOOT both have the pattern ABBA; a cipher word with that pattern is one of a very small set. Doubled letters are rarer than people expect — 44 of the 76 sayings here contain one at all — and when you find a doubled pair it is usually LL, SS, EE, OO or TT.

Only as a shortlist. The famous ordering — E T A O I N S H R D L U — is a long-run average over enormous quantities of text, and the sayings here are 22 to 42 letters long, 33 on average. At 12.7% you would expect E about four times in 33 letters, and a difference of one or two occurrences is ordinary noise. It is common for T or O to out-count E in a single sentence, and the frequency panel will happily tell you so.

Use it the right way round: the most frequent symbol is probably one of E, T, A or O, and the symbols that appear once are probably not. Test the guess against a word, not against the count — if the commonest symbol is the last letter of a four-letter word ending your sentence, E is a far better bet than T.

Every puzzle is a pure function of a number. The seed picks the saying, a second stream derived from it builds the key, and the same number gives you the identical puzzle on any device, forever — which is how puzzle #48213 can be shared with no account and no server. The key is drawn by rejection sampling from all derangements, with a constructive fallback so a key with a fixed point in it is not merely unlikely but impossible.

The difficulty dial is repetition, not length. A long saying built from twelve symbols repeats each one three times, so counts mean something and a wrong guess contradicts itself quickly; a short saying built from eighteen gives most symbols once, and there is nothing to count. The ratio across this corpus runs from 0.333 to 0.682, and the halves either side of the median are what Gentle and Expert draw from.

No. All seventy-six were written for this game: plain, unattributed proverbs and observations of the a small leak will empty the largest bucket sort. Nothing is quoted from anyone, and nothing is lifted from a quotation collection. That is a deliberate choice rather than a limitation — a cryptogram needs ordinary English with ordinary letter statistics, and a proverb is exactly that, while a famous quotation is often recognised from three words and then simply read rather than solved.

Every word of every saying is checked against the same public-domain ENABLE word list the other word games here use, so a typo or an invented word cannot reach a puzzle. If you like this kind of deduction, word search and sudoku run on the same principle: constraints you can check, and never a guess you cannot justify.