Bart Massey 2025

Construct all five-letter-by-five-letter word squares from a given dictionary under various constraints.

(Note: Jim Blandy quickly constructed a much faster solver the night after I gave a talk about this. It is a clever approach using prefix tries rather than state-space search. [He is clearly smarter than I am.] https://github.com/jimblandy/jimb-ws5)

Here is an example of a 5×5 canonical double word square:

mores
uvula
siren
enact
delta

This is a word square, since every row and column is a word from the dictionary used in construction.

This is a double word square, since no word is used more than once.

This is a canonical word square, since row one is a lexically-earlier word than column one. (The transpose of any word square — flipping it across the diagonal — is also a word square. We count these as uninterestingly different and take the canonical one as the representative.)

Build and run this Rust program with cargo run --release.

Use cargo run --release -- --help to get help with possible arguments.

By default, the program uses usa_5.txt as the dictionary, runs silently, and saves results into squares.json. These things can be changed with program arguments.

analyze.py checks and cleans up a squares.json file.

As of this writing, on my home box, this program completes in about 1.5 minutes.

Times on my home box (AMD Ryzen 9 3900X):

• Naïve algorithm: did not finish.
• First most-constrained search: 60m35s.
• Added hit cache for cross-fit and count cache for best-pos: 15m00s.
• Added de-doubling (doubly checks): 15m00s.
• Added de-transposition (canonicity checks): 14m08s.
• Added split dictionary for checks: 4m52s.
• Added split dictionary for search
  • Full: 1m56s.
  • Double canonical: 1m25s.

On my laptop (Intel Lunar Lake Core Ultra 7 258V) the runtime of the current version is 56s.

Generating full squares is about 80M nodes. Double-canonical is about 60M.

This crate is set up to profile with cargo flamegraph --release. You'll want to run systctl.sh on Linux to get access to programming features.

There are a couple of flame graphs in the artifacts/ folder.

Thanks to Gene Welborn for introducing the problem and providing a reference dictionary.

Thanks to the author of the caches lib crate for nice caches.

This work is made available under the "MIT License". See the file LICENSE.txt in this distribution for license terms.