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Every Target Puzzle

March 15, 2015

This post is for those who would like to do Target puzzles with larger word counts.

I have made a list of every possible Target puzzle. There are over 2500 Targets with word counts of 100 or more (not including obscure words). Why don’t we see Targets like these, especially on weekends? Contact your newspaper and tell them what you want!

Target rules

For those new to these puzzles, each Target places letters into a 3×3 grid and asks the reader for a list of words made from those letters where

  • each word is at least four letters in length
  • each word always includes the grid’s central letter
  • the list excludes plurals ending in ‘S’
  • the list contains at least one nine letter word

For example, for the letters

I L C
O Y R
S U U

an ‘excellent’ level list of non-obscure words (i.e. those in SIL – see below) would include
cloy, cosily, cosy, CURIOUSLY, curly, lousy, lyric, oily, rosily, rosy, sourly, surly, usury, your, yours
but exclude plurals (or similar – see below) such as
coils, curs, curios, lyrics, roils

If we allow non-obscure and obscure words (from SOWPODS – see below), then we would also add
coly, cory, corylus, crusily, crusy, lory, loury, ricy, roily, ruly, scry, sluicy, soily, syli

My mother (Hi Mum!) is a very keen Target puzzler, frequently getting more than the (newspaper defined) ‘excellent’ number of words. She often complains that there only 20 or 30 words to find. Others (Hi Peter!) are quite happy with, say, 15 as the ultimate target. I think it depends on the optimum length of time the puzzler wants to spend on the puzzle.

So I started wondering how many (or how few) words there could be in one Target. Of course, it all depends on which words are in our large word list.

I have based all the following data on

  •  SOWPODS, the official word list used in Scrabble tournaments outside North America. See here for the list in full. I used SOWPODS as my main Target word count generator because (a) it is associated with the oldest widely played word game and (b) it is the largest commonly accepted and available word list. OK, OK, the fact that it is the larger list is the main reason.
  • SIL English Wordlists (referred to below as SIL), with their full text file here. I chose this list because it’s (a) free and (b) about the right size, in that it produces word counts about 25% above the top end of newspaper target numbers, but I know you wanted a challenge.

(There are other lists, such as the Enhanced North American Benchmark Lexicon, a public domain list used in many games, such as Words With Friends. In size, this falls between the two lists above. There is also the extremely good Wordsmith anagram page, whose word counts seem to be similar to (i.e. within 5%-10% of) those (The Age) ‘excellent’ targets.

The Word List(s)

Looking only at Target words (those with four to nine letters), SOWPODS has 153886 and SIL has 106346.

As mentioned above, the Target word lists (unfortunately for our purposes) exclude plurals ending in ‘S’.

Excluding aardvarks and acres is simple enough.

On the other hand, Targets often include words such as alas (which is also the plural of ala) but exclude taxis (which is also a singular noun) – perhaps because the plural alas and the singular taxis are both obscure. And what to do with series, which is both singular and plural? In general, it seems that if a word can be plural (i.e. has a singular form within a given word set), then it’s excluded.

Moreover, they also seem to exclude words such as abdicates and abates, which are not plurals, but the third person singular forms of the corresponding verbs.

In any case, as far as trying to accurately distinguish words which should be excluded from those which should not, well, it turned out to be quite a lot of work.

So, in all that follows, I estimate that I have ‘wrongly’ categorised perhaps 50 words (in or out of the list). Still, I am using my best guess as to the list of allowable words, and will not keep saying that I am doing so.

Using these quirky rules, I arrived at the following word counts:

Letters

Full lists

Used lists

 SOWPODS

SIL

 SOWPODS

SIL

4

5454

3130

4461

2354

5

12478

6919

8873

4623

6

22157

11492

16205

8236

7

32909

16882

22580

11562

8

40161

19461

27381

13226

9

40727

16693

26846

10291

Total

153886

74577

106346

50292

In both lists, roughly one in every three words is a plural ending in ‘S’.

Target statistics

Each distinct letter in each nine letter word makes a distinct Target. For SOWPODS, the total number of Targets is 187749, an average of 6.99 for each distinct set of nine letters; the corresponding figures for SIL are 71262 and 6.92.

Some summary statistics of word counts:

SOWPODS SIL
Maximum 515 284
Average 90 51
Median 77 43
Mode 54 25
Minimum 1 1

A comparison of word counts for particular targets suggests that the top (‘excellent’) targets in the newspapers I read tend to be about 40%-45% of those from the SOWPODS word list.

Statistical interlude for senior secondary maths students

I know this post is stretching the ‘maths’ theme of this blog, so here is a sop to that.

(You can skip this bit if you like, unless you are indeed a SSMS, in which case read on…)

More detailed statistical measures of word counts are as follows:

SOWPODS SIL
Maximum 515 284
Minimum 1 1
Range 514 283
Average 90 51
St Dev 58 33
Q1 48 27
Median 77 43
Q3 118 67
IQR=Q3-Q1 70 40

Notes:

1. Skewness
The distribution of word counts is positively skewed. As would be expected for a positively skewed distribution,
        Mode < Median < Mean.

2. Outliers
Of the 187749 SOWPODS Targets, 6073 or 3,2% have word counts greater than 223=118+1.5×70. These word counts are – formally speaking – outliers, having counts above the upper fence. As the low fence is less than zero, there are no low outliers. That said, we would not normally use the notion of outliers with such large sample sizes, at least not in terms of box plot displays of outliers.

Exceptional cases

What follows is a selection of Targets which are extreme in some sense, having the most or least of a particular property.

Beneath each Target are specified
      central letter : SIL word count / SOWPODS word count
if the letters are rearranged to allow each indicated central letter. SIL counts are not provided if there is no SIL nine letter word for those letters.

1. Highest word count Targets

The following are the Targets with some of the largest SOWPODS word counts.

P N T
S E A
R L I

E: – / 515
A: – / 488

 
T G L
S E R
A N I

E: 260 / 493
A: 217 / 491

 
T N D
R E L
G I A

E: – / 481
A: – / 458

         
S D I
L E E
T A R

E: – / 469
A: – / 355

 
R T L
I E S
M N A

E: – / 467
A: – /441

 
I D T
A E E
R N S

E: – / 467
R: – / 363

See below for solutions. One of the nine letter words is in SIL, though I think it’s a less common word than two or three of the other words here.

2. One word Targets

There are 7 Targets whose only SOWPODS word is the nine letter word:

O U E
S X S
C U C

X: – / 1

G G G
O X O
B L E

X: – / 1

M U M
I V I
L U P

V: – / 1

I I I
O X U
L S V

X: – / 1

O O O
M Q N
E C U

Q: – / 1

O S O
I Q I
U L U

Q: – / 1

N T B
O X O
G S R

X: 1 / 1

See below for solutions. None except the last are common words (i.e. in SIL).

There are also 15 SIL Targets which have only the nine letter word in the list:

N T B
O X O
G S R

X: 1 / 1

T C M
U J A
G I D

J: 1 / 2

I I W
S C M
T T I

C: 1 / 2

I E I
B Z R
H Y D

Z: 1 / 3

I R M
R Z E
C E E

Z: 1 / 3

S L E
R Q U
U U O

Q: 1 / 3

B I U
G Q N
B I L

Q: 1 / 3

O N O
R Z P
O S O

 Z: 1 / 3

T E I
C Z M
I V I

Z: 1 / 3

H H H
A U A
I U C

U: 1 / 4

B K T
I M B
I U Z

M: 1 / 4

E E E
L Z L
P I T

Z: 1 / 5

O N O
R Z P
O T O

 Z: 1 / 5

E H T
I Z O
T G E

Z: 1 / 6

R A R
P V I
H A B

V: 1 / 8

In my humble opinion, some of the nine letter words above are rather obscure – but not according to SIL, so there they are.

3. Targets with most 9 letter words

The following are the Targets with four (the maximum) or three 9 letter words in SIL.

Beneath each Target, the numbers in parentheses are respectively the SIL and SOWPODS counts for nine letter words.

Note: In each case, the selected central letter gives the highest total word counts for those nine letters (as shown below). The central letter is not otherwise relevant for this category.

C I A
N R E
T R G

153 / 250 (4 / 4)

S G S
I E A
N R P

110 / 210 (3 / 5)

R I A
E T H
S T E

135 / 232 (3 / 4)

E L R
N A G
I H T

164 / 375 (3 / 4)

O L I
C L Y
P A T

73 / 120 (3 / 3)

A E I
O N U
C D T

109 / 211 (3 / 3)

B E B
S R I
T U L

83 / 133 (3 / 3)

T S C
A T N
I E S

75 / 142 (3 / 3)

R I T
A N O
N C E

151 / 274 (3 / 3)

N I C
R E O
G S T

162 / 275 (3 / 3)

N N R
G E D
A E I

116 / 236 (3 / 3)

S N G
L I N
E T I

77 / 138 (3 / 3)

T C I
A E L
V U R

155 / 257 (3 / 3)

P M G
R O N
H A O

54 / 100 (3 / 3)

S R G
P I I
E R N

68 / 118 (3 / 3)

4. All words beginning with central letter

This is a very restrictive condition, so the word counts are quite low.

Each Target below has exception counts in parentheses, i.e. the SIL and SOWPODS word counts for words beginning with letters other than the central letter.

SIL top 3:

P E M
L C E
R L O

25 / 39 (0 / 2)

D O L
M F M
E X U

19 / 25 (0 / 2)

E O F
L H L
P Y U

16 / 26 (0 / 4)

SOWPODS top 3:

M Y X
L C P
L E O

– / 26 (- / 0)

L N L
I J O
T G Y

– / 22 (0 / 0)

R O W
R C B
E R Y

– / 18 (- / 0)

Note that the word counts for SIL and SOWPODS are not that different.

5. No words beginning with central letter

This is the opposite to the previous category. With up to eight choices for the initial letter in any given Target, the word counts are also much higher.

Each Target below also has exception counts in parentheses, i.e. the SIL and SOWPODS word counts for words which do begin with the central letter.

SIL top 3:

I R L
K E N
P D S

133 / 223 (0 / 3)

M T A
O E O
C R D

129 / 186 (0 / 3)

T R T
D E O
R C A

124 / 180 (0 / 2)

Interestingly, 37 of the top 38 SIL entries here have ‘E’ as the central letter.

SOWPODS top 3:

T U B
A E F
D O L

96 / 171 (0 / 0)

T D M
B E A
U L A

89 / 156 (0 / 0)

O B A
P E T
A D L

86 / 149 (0 / 0)

6. Words found in most Targets

This takes the view from the other end. That is, which words appear in most Targets? Note that SIL words are in bold italics.

Word(s)

SIL

SOWPODS

rein, rine

8869

19961

rite, tier, tire, trie

8052

19625

nite, tine

8423

18734

aine, eina

18386

aret, rate, tare, tear

7268

18249

site, stie

7926

18222

rise, seir, sire

7178

17161

sien, sine

6699

17111

gien

16810

ilea

16102

7. Words not found in any Targets

Conversely, some words are not found in any Targets.

Word length

SIL SOWPODS

Words in no Targets

Total

%

Words in no Targets

Total

%

4

15

4459

0.30%

15

4459

0.30%

5

120

8953

1.30%

120

8953

1.30%

6

717

16529

4.50%

717

16529

4.50%

7

3198

22538

14.20%

3198

22538

14.20%

8

12121

27328

44.30%

12121

27328

44.30%

The four letter words not found in any Targets are:

SIL

buzz, foxy, hadj, hajj, jamb, java, jeez, jiff, jinx, john, jowl, juju, qoph, wavy, waxy

SOWPODS

foxy, fozy, hajj, jaxy, jazy, jeff, jiff, juju, juku, jynx, waxy, yuky, yuzu, ziff, zizz

Note that each of the words in the SOWPODS list contains at least one of ‘J’, ‘Y’ or ‘Z’ (so jazy had no chance :-))

8. Eight letter words in most nine letter words

The word angriest and its anagrams (rangiest and the SOWPODS-only angstier, astringe, ganister, reasting, stearing, and tasering) are remarkable in at least two ways.

Firstly, there are more anagrams (excluding plurals ending in s) for this eight letter group than any other.

Secondly, the letters of these words make at least one nine letter word with the addition of each of 9 (SIL) /18 (SOWPODS) different letters, for a total of 11/29 nine letter words:

Added letter Words
SIL SOWPODS
B BREASTING
C RECASTING
D ASTRINGED
E RESEATING
STINGAREE
G RESTAGING
I GRAINIEST
GRANITISE
SERIATING
K STREAKING
L GNARLIEST
RESLATING
M MASTERING
STREAMING
N GANNISTER
O ORANGIEST
P REPASTING
TRAPESING
R ARRESTING ASTRINGER
RASTERING
SERRATING
S ASSERTING
T RESTATING ASTERTING
RETASTING
U SIGNATURE
W WASTERING
Y ESTRAYING
Total 11 18

Solutions

As above, SIL words are in bold italics.

1. Highest word count Targets

STRAPLINE  

GNARLIEST
RESLATING

 

TRIANGLED
TREADLING

         

LATERISED

 

MISLEARNT

RESINATED

2. One word Targets

SIL one word Targets

STRONGBOX

JUDGMATIC

WITTICISM

HYBRIDIZE

MERCERIZE

QUERULOUS

QUIBBLING

SPOROZOON

VICTIMIZE

CHIHUHUA

KIBBUTZIM

PELLETIZE 

PROTOZOON GHETTOIZE VIBRAHARP

SOWPODS one word Targets

EXSUCCOUS GOGGLEBOX IMPLUVIUM
LIXIVIOUS MONOCOQUE SILIQUOUS
STRONGBOX

3. Targets with most 9 letter words

CRATERING
RECRATING
RETRACING
TERRACING

ASPERSING
GRAPINESS
PREASSIGN
PREASSING
REPASSING

EARTHIEST
HEARTIEST
HESITATER
HETAERIST

EARTHLING
HALTERING
HEARTLING
LATHERING

ALLOTYPIC
OPTICALLY
TOPICALLY

AUCTIONED
CAUTIONED
EDUCATION

BURBLIEST
RUBBLIEST
STUBBLIER

CATTINESS
SCANTIEST
TACITNESS

CONTAINER
CRENATION

NARCOTINE

CORSETING
ESCORTING
SECTORING

ENDEARING
ENGRAINED
GRENADINE
ENLISTING
LISTENING
TINSELING

LUCRATIVE
REVICTUAL

VICTUALER

MONOGRAPH
NOMOGRAPH

GRAMOPHON
REPRISING
RESPIRING
SPRINGIER

4. All words beginning with central letter

SIL top 3:

COMPELLER

FLUMMOXED

HOPEFULLY

SOWPODS top 3:

COMPLEXLY

JOLTINGLY

CROWBERRY

5. No words beginning with central letter

VAPORISED

RESHAPING

REDEPOSIT

and

OUTFABLED

AMBULATED

ADOPTABLE

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