Five 5-Letter Words, 25 Unique Letters
an exhaustive wordle-universe experiment (a love letter to bitmasks)
The original question is deceptively small:
can you find five 5-letter words that don’t share any letters?
If you can, you’ve covered 25 unique letters of the alphabet… which means exactly one letter is missing.
Most sane people find one cool set, nod, and move on with their lives. Stewart Labs did not do that.
If you can, you’ve covered 25 unique letters of the alphabet… which means exactly one letter is missing.
Most sane people find one cool set, nod, and move on with their lives. Stewart Labs did not do that.
“Some men want to watch the world burn.
I just want to know which letter refuses to cooperate.”
— Jason
The Real Question
Instead of “find a solution,” we asked:
For each letter A–Z, can that letter be the missing one — while still finding five disjoint 5-letter words?
In other words, we run 26 experiments:
- Exclude all words containing the chosen letter
- Filter to 5-letter, alphabetic words with no repeated letters inside the word
- Try to assemble five words with no letters in common
- Repeat until we find a solution… or prove there isn’t one
Methodology (in human terms)
Words are converted into a 26-bit mask (one bit per letter a–z). That makes overlap checks fast:overlap? (maskA & maskB) != 0
We used depth-first backtracking with aggressive pruning.
And importantly: these results are from a fully exhaustive search
(no timeouts, no caps).
Corpus: Wordle answers + allowed guesses (12,971 raw words), filtered + deduped by unique letter masks.
Results
After an exhaustive search for all 26 letters, only three letters can be the missing one:
Possible missing letters: J, Q, X
Impossible missing letters: everything else (including all vowels)
Impossible missing letters: everything else (including all vowels)
Missing letter: J
SOLUTION
vozhd · cylix · brung · waqfs · kempt
time: 72.470s · nodes: 300,134
Missing letter: Q
SOLUTION
nymph · fjord · vibex · waltz · gucks
time: 519.123s · nodes: 9,332,392
Missing letter: X
SOLUTION
jumby · vozhd · waqfs · prick · glent
time: 0.146s · nodes: 490
Everything else
NO SOLUTION
In the Wordle dictionary, there are no valid 5×5 / 25-letter sets with any other missing letter.
Fun fact: excluding Z still required exploring 59,625,789 backtracking states before the solver could finally say “nope.”
Fun fact: excluding Z still required exploring 59,625,789 backtracking states before the solver could finally say “nope.”
The Full Exhaustive List (Time / Nodes)
This is the “we actually checked” evidence. No vibes were used in the making of this table.
A No Solution time: 231.025s nodes: 6,133,661
B No Solution time: 1584.178s nodes: 34,438,007
C No Solution time: 1138.579s nodes: 24,279,594
D No Solution time: 1200.108s nodes: 26,286,157
E No Solution time: 247.332s nodes: 6,228,058
F No Solution time: 2092.142s nodes: 41,649,091
G No Solution time: 1540.091s nodes: 33,057,861
H No Solution time: 1185.113s nodes: 24,474,276
I No Solution time: 355.577s nodes: 7,803,217
J SOLUTION time: 72.470s nodes: 300,134
K No Solution time: 1576.294s nodes: 32,168,299
L No Solution time: 810.414s nodes: 18,043,995
M No Solution time: 1391.697s nodes: 28,755,253
N No Solution time: 837.847s nodes: 18,069,593
O No Solution time: 343.727s nodes: 7,700,724
P No Solution time: 1486.652s nodes: 30,385,476
Q SOLUTION time: 519.123s nodes: 9,332,392
R No Solution time: 643.156s nodes: 15,403,751
S No Solution time: 357.689s nodes: 9,228,126
T No Solution time: 918.130s nodes: 20,294,329
U No Solution time: 462.880s nodes: 10,665,282
V No Solution time: 3023.477s nodes: 56,392,221
W No Solution time: 2040.576s nodes: 39,758,956
X SOLUTION time: 0.146s nodes: 490
Y No Solution time: 865.996s nodes: 17,702,176
Z No Solution time: 3261.280s nodes: 59,625,789
What’s Next
The Wordle universe is a curated dictionary, not “all English.” Next phase: run the same experiment on a larger corpus (SCOWL or similar) and see what changes.Best case: new missing letters become possible. Worst case: I discover yet another reason to buy a faster CPU.