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 |
-
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”. ↩