Unique letter patterns in words

The word Mississippi has a unique pattern of letters. If you were solving a cryptogram puzzle and saw ZVFFVFFVCCV you might guess that the word is Mississippi.

Is the pattern of letters in Mississippi literally unique or just uncommon? What is the shortest word with a unique letter pattern? The longest word?

We can answer these questions by looking at normalized cryptograms, a sort of word signature. These are formed by replacing the first letter in a word with ‘A’, the next unique letter with ‘B’, etc. The normalized cryptogram of Mississippi is ABCCBCCBDDB.

The set of English words is fuzzy, but for my purposes I will take “words” to mean the entries in the dictionary file american-english on my Linux box, removing words that contain apostrophes or triple letters. I computed the cryptogram of each word, then looked for those that only appear once.

Relative to the list of words I used, yes, Mississippi is unique.

The shortest word with a unique cryptogram is eerie.

The longest word with a unique cryptogram is ambidextrously. Every letter in this 14-letter word appears only once.

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