Experiments with Knuth's 5,757 five letter words. https://charlesreid1.com/wiki/Five_Letter_Words
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This repository contains Donald Knuth’s GraphBase list of five-letter words,
as well as scripts to run various combinatoric experiments,
graph algorithms, and other algorithms to explore the
relationships among these words.

The list of words comes from [1] and is in the public domain.

Get Words

A Python program that contains a method for getting all of the five letter words from a file,
and that’s about it.

Warm Up Exercises

Exercises 26-37 of Knuth’s Volume 4 Fascile 0 are intended as a warm up to get to know
the SGB five letter word list. Solutions to these exercises are listed below.

distinct.py- computes the number of SGB words containing exactly k distinct letters.

diff_by_one_fixed.py - (fixed 2019-03-09) computes the number of words in the SGB
that are off by a single letter in each position. An example is rover and spuds.
Each corresponding letter is only different by one: r -> s, o->p, and so on.
This uses recursive backtracking to generate possible matches for each word, and
uses a hash table to check for their existence in the original word set.

There are 38 such pairs in the SGB.

Also see Five Letter Words
on the charlesreid1.com wiki.

diff_by_n_fixed.py - (added 2019-03-10.) using the corrected approach (above) to
computing differences by 1, this generalizes the calculation to words that are different
by a distance d for each letter position.

Also see Five Letter Words: Part 4: Revisiting Diff by One
(blog post) on charlesreid1.github.io.

euclidean_distance.py - computes the euclidean distance between two words. This uses
the traditional Euclidean distance definition but reinterprets distance to mean edit distance.

lexico.py - find words that are sorted by lexicographic order (front to back, a-z).

palindromes.py - look for five letter words that are either a palindrome, or a palindrome pair.


diff_by_n.py - computes words in SGB that have an edit distance of n.

reverse_lexico.py - variation on lexico.py that finds words whose letters are in
reverse lexicographic order.

Letter Coverage

letter_coverage.py - computes coverage of the alphabet (minimum number of words required
to provide X letters of the alphabet)

Knuth mentions, in the text, a couple of facts about how many words cover how much
of the alphabet. We authored a dynamic program to compute precisely this - given a
number of letters N from the alphabet, this program computes the minimum number of
words it takes to cover all N letters.

Also see Letter Coverage
page on the charlesreid1.com wiki.


  1. Knuth, Donald. The Stanford GraphBase: A Platform for Combinatorial Computing. New York: ACM Press, 1994.