Words with no proper subwords

Dan Graves visited us on a picket line recently, and told us of a word game he’d got from Tash Cowley: what is the longest word you can think of, none of whose proper substrings are words of three or more letters? For these purposes, proper nouns and abbreviations are not considered to be words. Thus, for example, famously doesn’t work because it has two substrings which are words: famous and sly.

Having spent some time on a picket line thinking about it, I rapidly wrote some code in Haskell to check it.

I ran it on the standard spellchecking “ispell” wordlist provided by Debian (at /etc/dictionaries-common/words); this has 104,334 words, of which 63,737 consist only of lowercase letters without punctuation. I found the following results:

• The longest words found were 13 click for spoilers letters long.

• These words were aristocracies, beneficiaries, physiognomies, and sanctimonious. click for spoilers.

• There were also words of one fewer letter than that, which were complaisance, compulsories, compulsorily, deficiencies, efficiencies, and plutocracies. click for spoilers.

Of course, the answer is strongly dependent on which strings are, and which strings are not, considered to be words. Using a bigger wordlist will give more candidates, but also more grounds for ruling candidates out. Thus I re-ran the experiment using two of the Moby word lists:

• Using the list of 113,809 words that form the first edition of the Official Scrabble Players Dictionary (of which 113,724 consist only of lowercase letters with no punctuation), the longest words had the same length as with the ispell dictionary: aristocracies and sufficiencies. The differences between the two sets of answers is explained as follows: sufficiencies is not in the ispell dictionary, and bene, nom and mon are in the OSPD and thus remove beneficiaries, physiognomies and sanctimonious respectively. click for spoilers.

• Using the big list of 354,984 words (of which 350,630 consist only of lowercase letters with no punctuation), the longest word had the same length again, but there was just one of them (not a word in frequent use on my manor): iliococcygian. There was also a twelve-letter word, zygophyceous, which is also rarely on the tip of my tongue. click for spoilers.