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I'm wondering if there's a set of four 7-letter words that employ all 26 English letters. That's 28 letters total, allowing for 2 duplicates. I would even count getting 25 a win (see below for my 22- to 24-letter sets). Please use YAWL for the wordlist. Some of my by-hand (and stolen) attempts [with letters missed] include:

  • Trypsin Daglock Jewfish Overmix [BZQU]
  • Trypsin Daglock Jewfish Bezique [VMX]
  • Frankly Mezquit Jodhpur Waxings [BCV]
  • Bravely Muzjiks Fowlpox Thonged [CQ]
  • Bravely Muzjiks Fowlpox Ducting [HQ]
  • Bravely Muzjiks Fowlpox Cantdog [HQ]
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    $\begingroup$ @bobble See my only other post. Puzzle-creation was suggested; I'm new, so I's just followin' orders. $\endgroup$
    – Frisky Dingo
    Commented Aug 20 at 16:48
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    $\begingroup$ This seems to mostly be a request to write code for a specific task. $\endgroup$
    – xnor
    Commented Aug 20 at 23:27

3 Answers 3

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If you count 25 letters as a win,

Some of the 119 solutions I found are:
blocked jewfish quartzy vamping [X]
cowflap dryings jukebox mitzvah [Q]
jukebox swiftly vamping zorched [Q]

Here, none of the words has any duplicate letter itself.

Edit: the previous 119 solutions with no letter duplications in any word.

avyzing boxfish lockjaw trumped -q
avyzing cutwork foxship jumbled -q
avyzing dropfly jambeux thwacks -q
avyzing frichts jukebox wimpled -q
avyzing jumbled postfix whacker -q
avyzing jumbled postfix whicker -q
avyzing jumbler postfix whacked -q
bedwarf gazumps jonquil kvetchy -x
blocked jewfish quartzy vamping -x
blowzed faquirs jumping kvetchy -x
boxfish delving pickmaw quartzy -j
boxfish devling pickmaw quartzy -j
boxfish jacking quartzy wimpled -v
boxfish jangled pickmaw quartzy -v
boxfish jingled pickmaw quartzy -v
boxfish jocking quartzy wimpled -v
boxfish jumping quartzy wedlock -v
boxfish jungled pickmaw quartzy -v
boxfish quartzy vacking wimpled -j
boxfish quartzy vamping wedlock -j
boxfuls jacking mitzvah powdery -q
boxfuls jacking quartzy whomped -v
boxfuls jacking quartzy whumped -v
boxfuls jocking mitzvah powdery -q
boxfuls jocking quartzy whomped -v
boxfuls jocking quartzy whumped -v
boxfuls jumping kvetchy wizards -q
boxfuls jumping quartzy whacked -v
boxfuls quartzy vacking whomped -j
boxfuls quartzy vacking whumped -j
boxfuls quartzy vamping whacked -j
britzka complex jewfish ungyved -q
bruxing dropfly mitzvah wejacks -q
buxomly howfing jetpack vizards -q
bywords fluxing jetpack mitzvah -q
bywords fluxing mitzvah pajocke -q
cashbox muzjiks perving twyfold -q
cashbox muzjiks preving twyfold -q
cawings dropfly jukebox mitzvah -q
chametz dropfly jukebox wavings -q
chametz dwarves flyping jukebox -q
chametz flyping jukebox swarved -q
chawing dropfly jukebox zemstva -q
chawing dropfly jukebox zemstvo -q
chewing dropfly jukebox zemstva -q
chinwag dropfly jukebox zemstva -q
chinwag dropfly jukebox zemstvo -q
chometz dropfly jukebox wavings -q
chometz dwarves flyping jukebox -q
chometz flyping jukebox swarved -q
chowder flyping jukebox zemstva -q
chowing dropfly jukebox zemstva -q
clyping jukebox mitzvah swarfed -q
clyping jukebox wharfed zemstva -q
clyping jukebox wharfed zemstvo -q
cowards flyping jukebox mitzvah -q
cowflap droving jukebox zythums -q
cowflap dryings jukebox mitzvah -q
cowflap jambeux kything vizards -q
cowherd flyping jukebox zemstva -q
crazing jukebox twyfold vampish -q
cyprids flawing jukebox mitzvah -q
cyprids flowing jukebox mitzvah -q
cyprids fowling jukebox mitzvah -q
cyprids jukebox mitzvah wolfing -q
delving foxship qwertys zambuck -j
devling foxship qwertys zambuck -j
diptych farebox muzjiks wolving -q
driveby foxhunt gazumps lockjaw -q
dropfly hawbuck mezquit vexings -j
dropfly jukebox mitzvah scowing -q
dropfly jukebox mitzvah sowcing -q
dropfly jukebox schmalz vawting -q
dropfly jukebox schmelz vawting -q
droving jewfish planxty zambuck -q
expugns lockjaw thrived zombify -q
filberd hypoxic muzjiks vawting -q
filched jukebox qwertys vamping -z
fixedly muzjiks pibroch vawting -q
fjordic gazumps hawkbit vixenly -q
flexing jodhpur qwertys zambuck -v
flocked jambeux vawting zephyrs -q
fluxing jodhpur qwertys zambuck -v
flyping jambeux thwacks vizored -q
flyping jukebox mitzvah scowder -q
fopling jambeux kvetchy wizards -q
foxings jirbled mitzvah wickyup -q
foxship jacking quartzy wambled -v
foxship jacking quartzy wimbled -v
foxship jambing quartzy wedlock -v
foxship jangled qwertys zambuck -v
foxship jingled qwertys zambuck -v
foxship jocking quartzy wambled -v
foxship jocking quartzy wimbled -v
foxship jumbled quartzy vacking -w
foxship jumbled quartzy wacking -v
foxship jumbled qwertys vacking -z
foxship jungled qwertys zambuck -v
foxship quartzy vacking wambled -j
foxship quartzy vacking wimbled -j
frowned glyphic jukebox zemstva -q
frumped jukebox wavings zlotych -q
hutzpas jackleg mixdown verbify -q
jambeux twifold vacking zephyrs -q
jambeux twyfold vacking zephyrs -q
jodhpur swiftly vexings zambuck -q
jodhpur twyfold vexings zambuck -q
jukebox machzor pavings twyfold -q
jukebox perfidy schmalz vawting -q
jukebox perfidy schmelz vawting -q
jukebox perving schmalz twyfold -q
jukebox preving schmalz twyfold -q
jukebox proving schmalz twyfold -q
jukebox scherzi twyfold vamping -q
jukebox scherzo twyfold vamping -q
jukebox swarfed vamping zlotych -q
jukebox swiftly vamping zorched -q
jukebox twyfold vamping zorches -q
lockjaw provend quights zombify -x

And here is the frequency of the missing letter

q 78
v 22
j 12
x 4
z 2
w 1

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  • $\begingroup$ I believe that you posted this reply on another post when my previous account asked a similar question. Could you please possibly post that list of 119 in full, alongside the 8-letter word sets mentioned above? Thanks! $\endgroup$
    – Frisky Dingo
    Commented Aug 20 at 17:51
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    $\begingroup$ I will later, but at the mo the search is considering duplicate letters in a word to hopefully find 26 in all :) Note that the previous question does list all the 28 eight-letter words containing the whole alphabet. $\endgroup$
    – Weather Vane
    Commented Aug 20 at 17:53
  • $\begingroup$ You're a rock star! Much appreciated. For me: puzzling.stackexchange.com/questions/123459/… $\endgroup$
    – Frisky Dingo
    Commented Aug 20 at 18:00
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    $\begingroup$ (+1) I confirm your count of solutions that use only words without duplicate letters. $\endgroup$
    – RobPratt
    Commented Aug 20 at 19:59
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    $\begingroup$ I found no full-alphabet solutions even with letters duplicated in any word. Added the previous 25-letter solutions with no duplications. $\endgroup$
    – Weather Vane
    Commented Aug 20 at 22:27
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Via integer linear programming (https://puzzling.stackexchange.com/a/123475/65277), I found that the maximum is

25.

There are 515 such optimal solutions, such as:

avyzing fowlpox jumbuck threads

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    $\begingroup$ I confirm that there are no full-alphabet solutions even with letters duplicated in any word. $\endgroup$
    – Weather Vane
    Commented Aug 20 at 20:08
  • $\begingroup$ Thank you. Is there any possibility of posting here (or messaging me) the full list? $\endgroup$
    – Frisky Dingo
    Commented Aug 20 at 21:12
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Unfortunately there are none that employ all 26 letters.

public static void Main(string[] args)
{
    var words = File.ReadAllLines("C:\\pse\\yawl-master\\yawl-master\\yawl-0.3.2.03\\word.list")
                    .Where(w => w.Length == 7 && new HashSet<char>(w).Count >= 5)
                    .Select<string, (string word, int mask)>(w => new(w, CreateBitmask(w)))
                    .ToArray();

    int targetMask = (1 << 26) - 1;

    int mj, mk, m;

    for (int i = 0; i < words.Length - 3; i++)
    {
        if (i % 1000 == 0)
        {
            Console.WriteLine(i);
        }

        for (int j = i + 1; j < words.Length - 2; j++)
        {
            mj = words[i].mask | words[j].mask;
            if (BitsSet(mj) < 12)
            {
                continue;
            }
            for (int k = j + 1; k < words.Length - 1; k++)
            {
                mk = mj | words[k].mask;
                if (BitsSet(mk) < 19)
                {
                    continue;
                }
                for (int l = k + 1; l < words.Length; l++)
                {
                    m = mk | words[l].mask;
                    if (m == targetMask)
                    {
                        Console.WriteLine($"{words[i].word} {words[j].word} {words[k].word} {words[l].word}");
                    }
                }
            }
        }
    }
}

static int CreateBitmask(string word)
{
    int bitmask = 0;
    foreach (char c in word)
    {
        bitmask |= 1 << (c - 'a');
    }
    return bitmask;
}

// hamming weight
static int BitsSet(int i)
{
    i = i - ((i >> 1) & 0x55555555);
    i = (i & 0x33333333) + ((i >> 2) & 0x33333333);
    return (((i + (i >> 4)) & 0x0F0F0F0F) * 0x01010101) >> 24;
}
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  • $\begingroup$ Shame. Thanks for all! $\endgroup$
    – Frisky Dingo
    Commented Aug 20 at 18:59
  • $\begingroup$ Could you post both sets of results (with and without doubled letters)? $\endgroup$
    – Frisky Dingo
    Commented Aug 20 at 21:52

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