Group of four letters with the most words that can be made

Factual Questions
1

Hi SD,
The other day, while waiting for the bus, I passed the time away by looking at the stop sign across the street. I wanted to see how many words (1, 2, 3, or 4 letters) I could make out of the letters S,T,O, and P.

I found: STOP, SOP, SPOT, OPT, OPTS, TOP, TOPS, POST, POT, POTS, TO, SO, SOT, and O.

That’s 14 words.

My question is, is there any group of four letters that have MORE legitimate words that can be made out of them, never using a letter more than once in the creation of a word? Could you use an anagram program to find out?

Dave

2

On the top of my head, I can make more words out of the four most common letters A,E N,T:

A
An
At
Et
Ane (Yes, Scottish!)
Ant
Ate
Eat
Ent (Old English/Middle Earth; I know!)
Nae
Net
Tan
Ten
Ante
Neat

That’s 15, and I’m sure I have missed some!

3

^ Etna (, Mt.)

4

Plus En - as in the letter or a type of dash.

5

Actually, there are 22 words you could have made.

I consider it cheating, but some Scrabble ™ players use sites such as:

6

From a strictly combinatorial standpoint, one can assemble 64 groups of all possible sizes from a group of four letters: 4 one-letter groups, 43 = 12 two-letter groups, 432 = 24 three-letter groups, and 4321 = 24 four-letter groups. But, of course, relatively few of these groups are likely to be valid dictionary words.

This also assumes that no letters in the group are the same; if so, the number of distinct possible groups goes down.

7

Without cheating, I can clearly see that I missed the obvious “Tea” and (again, Scottish – I’m a big Robert Burns fan!) “Tae”.

8

I got these 17 from SEAT:

seat
teas
eats
sate
east
etas
sea
eat
ate
tea
sat
set
eta
as
et
at
a

And then wordfind.com adds a few for 25 total:
ates
seta
tas
sae
tae
ae
es
ta

9

n/m. I see “ae” was already mentioned.

10

This is fun, but maybe we should move to the Game Room?

11

Using a 172k-entry word list, I get the following.

All unique letter sets that make more than 20 words:



(25) A, AE, AS, AT, ATE, ATES, EAST, EAT, EATS, ES, ET, ETA, ETAS, SAE, SAT, SATE, SEA, SEAT, SET, SETA, TA, TAE, TAS, TEA, TEAS
(24) A, AE, AL, ALE, ALT, AT, ATE, EAT, EL, ET, ETA, LA, LAT, LATE, LEA, LET, TA, TAE, TAEL, TALE, TEA, TEAL, TEL, TELA
(24) A, AE, AH, AT, ATE, EAT, EATH, EH, ET, ETA, ETH, HA, HAE, HAET, HAT, HATE, HE, HEAT, HET, TA, TAE, TEA, THAE, THE
(24) A, AE, AR, ARE, ARES, ARS, ARSE, AS, EAR, EARS, ER, ERA, ERAS, ERS, ES, RAS, RASE, RE, RES, SAE, SEA, SEAR, SER, SERA
(25) A, AE, AS, AT, ATE, ATES, EAST, EAT, EATS, ES, ET, ETA, ETAS, SAE, SAT, SATE, SEA, SEAT, SET, SETA, TA, TAE, TAS, TEA, TEAS
(24) A, AE, AL, ALE, ALT, AT, ATE, EAT, EL, ET, ETA, LA, LAT, LATE, LEA, LET, TA, TAE, TAEL, TALE, TEA, TEAL, TEL, TELA
(24) A, AE, AH, AT, ATE, EAT, EATH, EH, ET, ETA, ETH, HA, HAE, HAET, HAT, HATE, HE, HEAT, HET, TA, TAE, TEA, THAE, THE
(24) A, AE, AR, ARE, ARES, ARS, ARSE, AS, EAR, EARS, ER, ERA, ERAS, ERS, ES, RAS, RASE, RE, RES, SAE, SEA, SEAR, SER, SERA
(23) A, AE, AR, ARE, ART, AT, ATE, EAR, EAT, ER, ERA, ET, ETA, RAT, RATE, RE, RET, TA, TAE, TAR, TARE, TEA, TEAR
(23) A, AE, AN, ANE, ANT, ANTE, AT, ATE, EAT, EN, ET, ETA, ETNA, NA, NAE, NE, NEAT, NET, TA, TAE, TAN, TEA, TEN
(23) A, AE, AM, AT, ATE, EAT, EM, ET, ETA, MA, MAE, MAT, MATE, ME, MEAT, MET, META, TA, TAE, TAM, TAME, TEA, TEAM
(23) EN, ENS, EON, EONS, ES, NE, NO, NOES, NOS, NOSE, O, OE, OES, ON, ONE, ONES, ONS, OS, OSE, SEN, SO, SON, SONE
(22) A, AE, APE, APT, AT, ATE, EAT, ET, ETA, PA, PAT, PATE, PE, PEA, PEAT, PET, TA, TAE, TAP, TAPE, TEA, TEPA
(21) A, AR, ART, AT, O, OAR, OAT, OR, ORA, ORT, RAT, RATO, ROT, ROTA, TA, TAO, TAR, TARO, TO, TOR, TORA
(21) ER, EROS, ERS, ES, O, OE, OES, OR, ORE, ORES, ORS, OS, OSE, RE, RES, ROE, ROES, ROSE, SER, SO, SORE
(21) A, AE, AL, ALE, ALES, ALS, AS, EL, ELS, ES, LA, LAS, LASE, LEA, LEAS, SAE, SAL, SALE, SEA, SEAL, SEL
(21) A, AE, AERY, AR, ARE, AY, AYE, EAR, ER, ERA, EYRA, RAY, RE, RYA, RYE, YA, YAR, YARE, YE, YEA, YEAR
(21) A, AE, APE, APER, AR, ARE, EAR, ER, ERA, PA, PAR, PARE, PE, PEA, PEAR, PER, RAP, RAPE, RE, REAP, REP
(21) A, AE, AM, AMEN, AN, ANE, EM, EN, MA, MAE, MAN, MANE, ME, MEAN, MEN, NA, NAE, NAM, NAME, NE, NEMA

Of the 14,950 4-letter sets possible, 5239 make no words, 1271 make only a single word, 974 make two words, …, and 1 set makes 25 words. The full table of making is here:



      1  25
      3  24
      4  23
      1  22
      6  21
      7  20
     19  19
     27  18
     40  17
     68  16
     89  15
    131  14
    174  13
    240  12
    328  11
    370  10
    524  9
    689  8
    792  7
    920  6
   1020  5
   1071  4
    942  3
    974  2
   1271  1
   5239  0