Prefix-suffix Bicliques
How many word fragments can we find that all fit together?
I saw this toy at the store:

It has five prefixes and five suffixes such that each pair forms a valid word.
| prefix | suffix |
|---|---|
| p- | -ad |
| b- | -at |
| m- | -ail |
| h- | -ay |
| r- | -ug |
Can we do better than 5 of each? I ran a quick search on a dictionary-consensus wordlist, and the best1 I could find was a 7x7:
| Prefix | Suffix |
|---|---|
| b- | -ad |
| d- | -ang |
| f- | -ate |
| g- | -ay |
| p- | -ear |
| r- | -ill |
| s- | -un |
I actually found a few dozen 7x7 sets. The one above seems well-suited to an actual toy, but the first one I found was the following, which would make for a beautifully stupid children’s toy:
| Prefix | Suffix |
|---|---|
| materia- | -l |
| rea- | -listic |
| rationa- | -lize |
| natura- | -list |
| socia- | -lization |
| nationa- | -lly |
| individua- | -lism |
There’s also a 7x8 set, but it has a few questionable word-pairs:
| Prefix | Suffix |
|---|---|
| b- | -ad |
| c- | -ake |
| h- | -ash |
| l- | -ay |
| m- | -ob |
| r- | -ock |
| s- | -oot |
| -ow |
And if we’re willing to use medical terminology, then here’s a 10x10:
| Prefix | Suffix |
|---|---|
| aden- | -algia |
| chondr- | -itis |
| desm- | -odynia |
| encephal- | -ography |
| hepat- | -oid |
| my- | -ology |
| neur- | -oma |
| odont- | -opathy |
| oste- | -osis |
| splen- | -otomy |
Other Musings
Can We expand on the original toy’s wordlist?
Yes and no.
There are no prefixes we could add that work with all five of the original suffixes
-ad,-at,-ail,-ay,-ug.
However, there are another 10 additional suffixes that work with p-, b-, m-, h-, r-:
-are, -ate, -atter, -ill, -ock, -od, -ole, -ound, -uff, -ush
Can we make a toy with only 3-letter words?
The original toy has one two-letter suffix, -ail, which means some of the resulting words are four letters long.
that’s a bit unsatisfying.
If they replaced -ail with -od, then the toy would be more symmetric.
Though “bod” and “mod” are admittedly questionable as words go…
Here’s an alternate set, which doesn’t have that problem, but does have a couple of its own odd or archaic words:
| Prefix | Suffix |
|---|---|
| d- | -ad |
| h- | -ay |
| l- | -id |
| m- | -ot |
| r- | -ug |
Here’s one with a couple “kid-friendly” naughty words - “pee” and “wee” which would paradoxically make for an excellent toy but also one that a toy company would be averse to selling.
| Prefix | Suffix |
|---|---|
| b- | -ad |
| l- | -ay |
| p- | -ee |
| s- | -et |
| w- | -it |
And here’s an alternative with 2-letter prefixes and 1-letter suffixes:
| Prefix | Suffix | ||
|---|---|---|---|
| ca- | -d | ||
| co- | -n | ||
| ma- | -p | ||
| ra- | -w | ||
| so- | -y | ||
| <!– | pa- | -t | –> |
Still not perfect. I understand what the toy designers resorted to -ail.
Can we make a toy with only 2-letter words?
No.
You can get a 3x4 set with two letter words if you’re willing to accept exclamations:
ah, am, an, ax, eh, em, en, ex, oh, om, on, ox
But there’s no 5x5 set.
Stop trying to make a better toy. Let’s make a worse one.
That result up above with words like “materia-listic” was pretty silly. I wonder how big I could force the words to be in a toy like this…
Turning to the wikipedia corpus (all words used on wikipedia), I found a 5x5 set where the minimum word length is 17 and the average is 18.8. But this cheats by using both British and American spellings.
| Prefix | Suffix |
|---|---|
| anthropomorph- | -izations |
| institutional- | -isation |
| mischaracter- | -ization |
| reconceptual- | -ising |
| recontextual- | -izing |
Here’s one that doesn’t rely on variant spellings. The minimum word length is only 16, but the average is 19.2. And wow! What a terrible list of words!
| Prefix | Suffix |
|---|---|
| otorhinolaryng- | -ological |
| psychopharmac- | -ologists |
| electrophysi- | -ologist |
| paleoanthrop- | -ologic |
| dendrochron- | -ology |
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By “best”, I mean largest NxN set. If we just wanted to know the largest NxM set period, then we would look at every word that ends in “s”. ↩