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I know a set of six 4-letter words without repeating a letter (i.e. using 24 different letters).

Here is an example:

gasp, verb, jinx, flow, duck, myth

Are there sets of words with no repeated letters and having

  1. four 6-letter words?
  2. five 5-letter words?
  3. three 8-letter words?

Bonus: Find a set of words (non-repeating letters) of sizes 1,2,3,4,5,6.

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Using words from the SOWPODS word list, it's possible to solve Q1 and Q2 but sadly not Q3. I checked this by creating a graph of k-letter isograms, connecting words with no shared letters, and searching for cliques.

Five 5-letter words

Lots of answers, all using obscure words: e.g.

brick, jumpy, vozhd, glent, waqfs
vibex, fjord, nymph, waltz, gucks
bling, jumpy, vozhd, treck, waqfs

Four 6-letter words

Lots of answers, some using slightly less obscure words: e.g.

jawbox, kvetch, flumps, drying
jumbly, dwarfs, kvetch, poxing
jawbox, fledgy, skrump, chintz

Three 7-letter words

Lots and lots of answers: e.g.

stumped, flyback, whoring
mucking, batfowl, zephyrs
jordans, phlegmy, fuckwit
overply, dumbing, thwacks

Two 10-letter words

blacksmith, gunpowdery
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Here's a set for the bonus question:

a
be
why
jump
flong (a type of mould used in relief printing)
tricks

The missing letters are:

dqvxz

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I have 2 possible answers for the four 6-letter words. Both were obtained by parsing a scrabble 6-letter word list, picking out words with few vowels, then checking to make sure there were 24 distinct letters.

blowzy, frumps, jading, kvetch
frowzy, jading, kvetch, plumbs

I attempted the same thing with five 5-letter words, but did not get a match.

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At the end of "Pangram Variations" (Word Ways, Feb. 1977, p.44), Ross Eckler gives the following examples:

For 1. (four 6-letter words): MUZJIK PEGBOX DWARFS LYNCHT

For 2. (five 5-letter words): FUDGY JAMBS PHLOX WRECK QVINT

Eckler says that Howard Bergerson came up with that set of 5-letter words in Webster's Second. His three-word example is of 7-letter words (JACKBOX FRESHLY DUMPING), suggesting that, even with a dictionary as large as Webster's Second, there is no set of three 8-letter words to be found.

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For the 1-letter bonus, there are two possible answers:

The first is that there are three different words:
A
I
O
Strictly speaking, these are the only one-letter words in English ("O" is an alternate spelling of the interjection "Oh").

The second answer relies on a more flexible meaning of "word": every letter can be regarded as a self-referential word. That is, as a word that identifies the letter, as in "C is for Cookie" or "The L Word". In this case, one can list 26 distinct words with no letters in common between any of them!

I'm currently working on the eight-letter question (and I want to do it without writing a search script), but as a hint to other solvers: there are only five vowels not including Y (which I just used as a word), so one of the eight-letter words will need to have only one "regular" vowel, and will probably need to use Y as a vowel. Some possibilities are BRIGHTLY GRYPHONS HYDRANTS PSYCHING SHREWDLY SPLOTCHY. It might be especially useful to use SCHMALTZ or SCHMALZY/SHMALTZY to use a Z.

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  • $\begingroup$ If I'm right that the only English 8-letter word containing a single vowel letter is strength, which isn't allowed because it's got two t's, then each of the three 8-letter words must have exactly two vowel letters. $\endgroup$ – h34 Jan 26 '15 at 21:02
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    $\begingroup$ @h34 I think strengths is the only English 9-letter word with only one vowel, but there are at least a few other 8-letter ones. For example, schmaltz, which is in my answer. That's the only one I know of with no repeating letters, though. $\endgroup$ – KSmarts Jan 26 '15 at 21:27
  • $\begingroup$ Thanks for this. I stand corrected. The longest one-vowellers in SOWPODS are two with nine letters (strengths, tsktsking) and 20 with eight (borschts, pschents, schmaltz, shrights, sprights, strength, tsktsked, twelfths, and 12 of the form sch----s borrowed from Yiddish or German), so going by their list schmaltz is the only one-voweller with eight or more letters and no repeats. $\endgroup$ – h34 Jan 27 '15 at 9:14
  • $\begingroup$ By the proper definition of a vowel as a phoneme, tsktsked has none at all! $\endgroup$ – h34 Jan 27 '15 at 9:23

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