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What English word has the most valid word substrings, no repeats?

Examples (I may have missed some words):

AIRSPACES: a, i, air, spa, space, spaces, pace, paces, ace, aces

DEMONETIZED: demo, demon, net, monetized, i, zed

INCANDESCENT: i, in, inca, can, a, an, and, descent, scent, ent

I realize long words may have an unfair advantage, such as PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS: mono, ultra, a, tram, am, micro, i, cop, volcano, can, an, no, con, on, is

so an alternate question would be: what word has the highest score of [sum of number of letters in all non-repeating substrings]/[length of word]

Thus, I am interested in these 3 categories:

  1. Word with most valid substrings
  2. Word with greatest character count of valid substrings
  3. Word with greatest [character count of valid substrings]/[word length]


Computer generated results are accepted.



Current Top Results:

(Mieliestronk)
1. INTERRELATIONSHIPS ; 23 substrings ; Jaap Scherphuis
2. INTERRELATIONSHIPS ; 136 characters ; Jaap Scherphuis
3. INTERRELATIONSHIPS ; 7.55 score ; Jaap Scherphuis
(SOWPODS)
1. DEFORESTATIONS , DISFORESTATIONS; 34 substrings ; Peter Taylor
2. BIPARTISANSHIPS ; 176 characters ; Peter Taylor
3. PREPOSSESSIONS ; ~12.29 score ; Peter Taylor

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    $\begingroup$ I think the open-ended tag fits well here. $\endgroup$
    – Mordechai
    Jul 11, 2017 at 4:16
  • $\begingroup$ Running at +5 at time of writing; I'm glad your question found its audience :) $\endgroup$
    – AndyT
    Jul 11, 2017 at 8:17
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    $\begingroup$ @AndyT Thanks again for helping me find the correct place to post this $\endgroup$
    – Cheeezburger
    Jul 11, 2017 at 9:30
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    $\begingroup$ I’m voting to close this question because open-ended puzzles are off-topic as of May 2019, and "word" isn't defined here anyhow so it isn't specified enough. $\endgroup$
    – bobble
    Jun 28, 2021 at 21:30

3 Answers 3

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I confess I wrote a small computer program to search for these words with the most subwords. I used a word list containing about 58000 relatively normal words, with "A" and "I" as the only 1-letter words. No doubt results will be very different if you include more obscure short words.

7 letters, 8 subwords totalling 20 letters, score 20/7 = 2.86:

ABANDON: A BAN BAND AN AND DO DON ON

9 letters, 12 subwords totalling 35 letters, score 35/9 = 3.89:

ABANDONED: A ABANDON BAN BAND AN AND DO DON DONE ON ONE NE

11 letters, 14 subwords totalling 52 letters, score 52/11 = 4.73:

ABERRATIONS: A ABE ABERRATION BE ERR RAT RATIO RATION RATIONS AT I ION IONS ON

12 letters, 18 subwords totalling 63 letters, score 63/12 = 5.25:

CHAMPIONSHIP: CHAMP CHAMPION CHAMPIONS HA HAM A AM AMP PI PION PIONS I ION IONS ON SHIP HI HIP

13 letters, 21 subwords totalling 84 letters, score 84/13 = 6.46:

CHAMPIONSHIPS: CHAMP CHAMPION CHAMPIONS CHAMPIONSHIP HA HAM A AM AMP PI PION PIONS I ION IONS ON SHIP SHIPS HI HIP HIPS

17 letters, 22 subwords totalling 109 letters, score 109/17 = 6.41:

GREATGRANDMOTHERS: GREAT GREATGRANDMOTHER RE EAT A AT GRAND GRANDMOTHER GRANDMOTHERS RAN RAND AN AND MOTH MOTHER MOTHERS OTHER OTHERS THE HE HER HERS

18 letters, 23 subwords totalling 136 letters, score 136/18 = 7.55:

INTERRELATIONSHIPS: I IN INTER INTERRELATION INTERRELATIONS INTERRELATIONSHIP ERR RE RELATION RELATIONS RELATIONSHIP RELATIONSHIPS ELATION A AT ION IONS ON SHIP SHIPS HI HIP HIPS

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  • $\begingroup$ Interesting results. Admittedly, I expected there to be more results with substrings consisting of words formed from separate word fragments, such as DEMON in DEMONITIZED, rather than simply splitting long words into its compound components. $\endgroup$
    – Cheeezburger
    Jul 11, 2017 at 9:37
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    $\begingroup$ @Cheeezburger: That may be partly because I used a word list with few obscure words, but more likely it's just that using the semantic components is more likely to build a meaningful word and if you have several components the number of potential subwords increases exponentially. Fragments of those components are unlikely to be as productive. Still in the last answer, the first S from -SHIPS was very productive, though RELATION->ELATION was not. $\endgroup$
    – Jaap Scherphuis
    Jul 11, 2017 at 11:05
  • $\begingroup$ What dictionary did you use? Does it have a name? $\endgroup$
    – Cheeezburger
    Jul 12, 2017 at 3:04
  • $\begingroup$ I'm not sure since I downloaded it ages ago. I think it was likely the corncob list to which I added the two 1-letter words I mentioned. $\endgroup$
    – Jaap Scherphuis
    Jul 12, 2017 at 7:03
  • $\begingroup$ @Cheeezburger: With this list PREPOSSESSIONS scores 7.42 (17 subwords, total length 104), BIPARTISANSHIPS scores 6.2 (20 subwords, total length 93) and DEFORESTATIONS scores 5.35 (19 subwords, total length 75). $\endgroup$
    – Jaap Scherphuis
    Jul 12, 2017 at 7:19
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I only tried one word but it took longer than I had expected, so I won't try another one for a while. Here goes.

relisted = 8
relist = 6
listed = 6
list = 4
sted = 4
lis = 3
ist = 3
ted = 3
el = 2
li = 2
is = 2
te = 2
re = 2
e = 1
i = 1
The ratio is 5.125

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  • $\begingroup$ Did you do this manually or computationally? $\endgroup$
    – Cheeezburger
    Jul 11, 2017 at 3:49
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    $\begingroup$ @Cheeezburger I did it by hand.I am sure you can find better words. $\endgroup$
    – stack reader
    Jul 11, 2017 at 4:05
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As Jaap observed, the results are quite different with a dictionary which emphasises short words. Specifically, I used SOWPODS, which doesn't have words longer than 15 characters but does have a lot of obscure short ones.

  1. Word with most valid substrings

    At 34 words and 14 characters:

    DEFORESTATIONS with substrings DE, DEF, DEFOREST, DEFORESTATION, EF, FOR, FORE, FORES, FOREST, FORESTATION, FORESTATIONS, OR, ORE, ORES, RE, RES, REST, RESTATION, RESTATIONS, ES, EST, ST, STAT, STATION, STATIONS, TA, TAT, AT, TI, IO, ION, IONS, ON, ONS

    It ties with the closely related 15-character word

    DISFORESTATIONS

  2. Word with greatest character count of valid substrings

    At 176 characters from a 15-character word:

    BIPARTISANSHIPS with substrings BI, BIPARTISAN, BIPARTISANSHIP, PA, PAR, PART, PARTI, PARTIS, PARTISAN, PARTISANS, PARTISANSHIP, PARTISANSHIPS, AR, ART, ARTI, ARTIS, ARTISAN, ARTISANS, ARTISANSHIP, ARTISANSHIPS, TI, TIS, IS, SAN, SANS, AN, SH, SHIP, SHIPS, HI, HIP, HIPS

  3. Word with greatest [character count of valid substrings]/[word length]

    At a ratio of 172/14 ~= 12.29

    PREPOSSESSIONS with substrings PRE, PREP, PREPOSSESS, PREPOSSESSION, RE, REP, REPO, REPOS, REPOSSESS, REPOSSESSION, REPOSSESSIONS, EPOS, PO, POS, POSS, POSSE, POSSES, POSSESS, POSSESSION, POSSESSIONS, OS, SESS, SESSION, SESSIONS, ES, ESS, SI, IO, ION, IONS, ON, ONS

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