How to solve a cryptogram

Start with the surprise: longer is easier

An easy cryptogram in this catalog averages 83.8 letters. A hard one averages 60.4. The hard puzzles are the short ones, by about a quarter, and this is the single most useful thing to understand about substitution ciphers.

The reason is that the puzzle is always 26 letters, whether the quotation runs to forty words or to eight. That means a longer quotation is not a bigger problem; it is the same problem but with more to go on. What matters is how much text there is per unknown. In the easy tier each distinct letter appears 4.4 times on average; in the hard tier, 3.1. Counting how many times a letter occurs can help you narrow it down when that count is four, five, or more. But at three and below, it doesn’t do much for you.

If short puzzles weren’t already hard enough just by being short, they also use more of the alphabet: 19.4 distinct letters against the easy tier's 18.9. More unknowns, less text to find them in. So if you’re picking a puzzle to learn on, pick a long one.

Counting letters is weaker evidence than you have been told

Every guide opens the same way: E is the most common letter in English, therefore the most common symbol is E. Across this catalog that is true in 51.9% of quotations. It is the best single guess available, but it’s barely better than a coin flip, so don’t be discouraged if it doesn’t work.

The cause is sample size rather than anything special about the quotations. The average gap between the most common letter and the runner-up is 2.3 occurrences. In 17.1% of these puzzles two or more letters are tied at the very top, so there is no most common symbol to point at. A frequency count over sixty letters ranks the alphabet roughly right and precisely wrong, which makes it good for ordering your guesses and dangerous as a pattern to follow every time.

So, count, but hold the count as a ranking of suspects, and let the evidence in the next three sections help you identify which is which.

The apostrophe is the only mark that gives you a letter

An apostrophe hands a letter over. The catalog contains 2,731 apostrophes followed by a letter, and 95.4% of the time that letter is one of seven: S, T, D, L, M, R, V. Two of them do most of the work. The letter after an apostrophe is T in 35.6% of cases and S in 31.9%, so two-thirds of the time an apostrophe signals one of those two letters.

“n’t” is even better, because it gives away two letters in one. A word whose last three symbols are letter, apostrophe, letter is very often that one, and it gives you N and T together. The catalog contains 952 of them, spread across 8.5% of all quotations.

This is also the clearest difference between the tiers, and it’s worth knowing which way the odds run before you go hunting. 28.9% of easy quotations carry an apostrophe followed by a letter; only 11.7% of hard ones do. When a puzzle “feels” easy, this is often why.

Short words come from a list, and the list is also short

A one-letter word is A or I. Not quite an absolute, but 99.5% of the 9,730 one-letter words in the catalog are one of those two, and the rest are initials and the occasional vocative O. Both are common letters, so placing one pays off immediately somewhere else.

Two-letter words are the ones worth memorizing. There are 30,776 of them here in 72 distinct forms, but only 26 forms account for 99%. In practice a two-letter word is a guess from about twenty-two, in order of how often they turn up here: to, of, in, it, is, my, be, as, he, me, no, at, we, on, so, if, do, by, or, an, up, am.

Notice what those are made of. Many of the letters in that list are among the most common in English, which is why a run of two-letter words unravels a puzzle so quickly: each one you solve is a letter that appears all over the rest of it.

“The”, honestly

Every guide tells you to look for “the.” That’s good advice, but here’s what it’s actually worth. 53.6% of these quotations contain the word “the” at all, and 18.5% of all three-letter words in the catalog are that one, comfortably ahead of “and” at 11.5%, and ahead of everything else by more.

The usual version of the advice is that a three-letter word appearing more than once is nearly always “the”, but that’s not really the case. 33.2% of quotations contain a repeated three-letter word, and where there is one, the most-repeated one is “the” 41.7% of the time, with “you” behind it at 14.5%. Three repeats or more and it rises to 53.5%, which is good, but still not much better than a coin flip.

Give it a shot because nothing else pays as well, but be careful. The thing that confirms it is not the repetition but the E: if the third symbol of your candidate “the” is also the most common symbol in the puzzle, then you have two pieces of evidence, and that’s worth more than either of them alone.

Word shape is the strongest evidence in the puzzle

A word's shape is its pattern of repeated letters, ignoring the letters themselves. “Letter” and “bottom” share a shape: six long, with the third and fourth the same as each other and the second and fifth the same as each other. That pattern survives encipherment perfectly, since it is the one thing a substitution cipher cannot hide, and it gets rare very fast as words get longer.

Measured over the 12,807 distinct words in this catalog, here is how far a shape narrows the field:

Check the last column. A five-letter shape leaves you choosing between seventy-ish words and is almost worthless by itself. A nine-letter shape leaves fewer than three options, and a quarter of nine-letter words have a shape that is unique among the nine-letter words here. By twelve letters, the shape simply is the word.

This is why the difficulty model counts a long word as making a puzzle easier, which is the opposite of what people expect. The longest word in a typical quotation runs about 8.8 letters in the easy tier and 9 in the hard one, long enough to be the best lead available. Find the longest word first and write its shape down before touching anything else.

Doubled letters are the same idea in miniature. The catalog holds 16,679 doubled pairs, and 95.5% of them come from the ten pairs English actually doubles: LL, EE, SS, OO, TT, FF, RR, NN, PP, MM. 59.5% are LL, EE or OO. A doubled symbol is a three-way guess wearing a twenty-six-way disguise.

What actually makes a puzzle hard: the letters that appear once

The largest single term in our difficulty score is the number of letters used exactly once, weighted by which letter it is. Nearly every quotation has at least one, 99.2% of them, so the question is never whether, but how many. The easy tier averages 2.6 of them, weighted; the medium tier 3.9; the hard tier 5.9.

A letter appearing once is invisible to every technique above. It has no frequency worth counting, it forms no pattern with itself, and you can only reach it from the word it sits in or by elimination once nearly everything else is placed. The cost is decided by which letter it is: a quotation whose only Q appears once is half solved by the U behind it, while a quotation whose only E appears once has ruined everybody’s opening move. In case you’re worried, know that the second case is genuinely rare; E is used exactly once in only 14 of the 10,106 quotations here. The ordinary version is five or six middling letters that simply never repeat, and that’s what a hard puzzle usually turns out to be.

Practically speaking, when you stall with three or four symbols left, stop looking for evidence because there isn’t any. Check the letters you have not used yet and fit them to the gaps by what makes a word.

An order of operations

All of the advice above is intentionally ordered by how much each move gives you for the effort it costs. That’s not the order the folklore teaches.

1. Apostrophes first. They are the only marks that hand a letter over. Look for “n’t”; failing that, take the letter after the apostrophe and try T, then S.
2. Then the longest word. Check its shape. If it repeats a letter, you have narrowed English to a handful of candidates before guessing anything at all.
3. Then the one- and two-letter words. A single letter is A or I. A pair is one of about twenty-two, and every letter you take from one is a common letter that turns up elsewhere.
4. Then count. Rank the symbols by frequency and treat the ranking as suspicion rather than fact. Use it to break ties between guesses the earlier steps have already narrowed.
5. Place a letter and read outward. A cryptogram is solved through words, not letters: every symbol you fix makes some other word nearly readable. Say the neighbors in your head, and abandon the guess the moment one of them becomes unpronounceable. Backing out quickly is most of the skill.
6. Finish by elimination. The last few letters are the ones that appeared once. They were never going to be found by counting.

How this site grades a puzzle

Every quotation here is scored from 0 to 100 on what its own letters give away. Below 44 is easy, 60 and above is hard, and the middle is everything in between. Length is not an input: the catalog is filtered to a narrow band of lengths before scoring, and as the first section explains, length runs the opposite way from what people expect in any case.

These are the inputs, in the order the model weights them:

Where to practice

There is a page on each tier, written from the same measurements: what makes one easy, what puts one in the middle, and what makes one hard. Between them they cover 10,106 quotations drawn from the curated collections, and no puzzle you have already solved is ever dealt to you again.

Start an easy cryptogram