Hard cryptograms

Shorter, and harder because of it

A hard cryptogram averages 60.9 letters, against the easy tier's 84. It is a quarter shorter and it uses more of the alphabet: 19.5 distinct letters, against 19.

That combination is the whole of it. More unknowns, less text to identify them from. Each distinct letter appears 3.1 times on average here, against 4.4 times in the easy tier, and a frequency count over three occurrences is noise. The counts still rank the letters roughly right, but not reliably enough to build on, and a solve that starts from a mis-ranked count has to be unwound later.

Letters that appear exactly once

The largest single term in the difficulty score is the number of letters used exactly once, weighted by which letter it is. This tier averages 5.8 against the easy tier's 2.5.

A letter appearing once is invisible to counting. It has no frequency, it forms no pattern with itself, and it can only be reached from the word around it or by elimination once the other twenty-odd are placed. A puzzle whose only E appears once has taken away the move everybody opens with. A puzzle whose only Q appears once has taken away nothing, and is half solved by the U behind it, which is why the score weights them differently rather than counting them.

And the usual footholds are missing

Only 10.6% of these carry an apostrophe followed by a letter, against 26.7% of the easy tier, so the one mark that hands a letter over outright is usually absent. 47.3% contain the word “the”, against 61.3%. They average 0.7 single-letter words and 2 two-letter ones, where the easy tier has 1.4 and 4.1.

Take those away and there is no opening move that is nearly free. What is left is the long words: this tier's longest word averages 9.1 letters, and a long word is the best evidence in a short cryptogram because its pattern of repeats is rare enough to be nearly unique. Doubled letters are the other one: English doubles about ten letters and no others, so a doubled symbol is a ten-way guess rather than a twenty-six-way one.

Expect to hold two or three hypotheses at once and to abandon most of them. That is what this tier is for. If you want the order to try them in, and the evidence for why counting letters belongs late in it rather than first, how to solve a cryptogram works through it.

This tier by the numbers

Averages over all 2581 puzzles, measured from the plaintext. The same measurements are taken for every puzzle in the catalog, so the three tiers can be compared line for line.

Who you will be reading

The hard tier draws most heavily on Jane Austen, Charles Dickens, Mark Twain, Arthur Conan Doyle, George Eliot and Thomas Hardy. Difficulty has nothing to do with who said a thing. An author appears in all three tiers depending on how each sentence happens to fall.

81 of this tier's 2581 puzzles are not quotations at all. They are authored facts — written for this site, each one checked against a named source — so they are dealt alongside the books and attributed to nobody.

How the grade is worked out

Each puzzle gets a score from 0 to 100, built from about a dozen metrics: how many letters it uses, how many of them appear only once, how many short words it contains, whether it has an apostrophe, whether E leads the frequency table. Below 44 is easy, 60 and above is hard, and the middle is everything else. The hard tier actually spans 60 to 93, averaging 66.7.

Length is not one of the inputs, and that is the part most people find surprising. Nor is vocabulary; a long word is easier, not harder, because its shape is rarer and therefore more identifiable.

The full model, covering every input, which way each one runs, and what the catalog says each is worth to a solver, is set out in how to solve a cryptogram.