Scrambled Alphabets in Word-Lists

,

the

abbre-

os

Angeles.)

UNRAKE

are

ompleted

ac-

~rb).

I

also

JS,

although

Nevertheless,

unsmoothened

distinct,

but

.NG

and

UN-

I,

since

this

::mr

attention

NLEDE,

from

mtry,

man.

I

CH

monster,

t

Russian

L

Y-

ELEOTHEROS

nate

his

re-

i.

With

typi-

;CARB,

found

:"

as

yet

as-

he

word

that

r

translators

om

the

'tra-

etting

pretty

ropean

mole.

leaving

War-

145

SCRAMBLED

ALPHABETS

IN

WORD-LISTS

A.

ROSS

ECKLER

Morristown,

New

Jersey

Arrange

the

letters

of

the

alphabet

in

a

specified

order,

and

imbed

these

in

a

list

of

words,

the

object

being

to

use

as

few

let-

ters

as

possible

in

the

word-list.

For

example,

if

the

letters

are

arranged

in

alphabetic

order,

and

one

is

restricted

to

boldface

entries

in

the

Merriam-Webster

Pocket

Dictiona

ry,

with

no

single-

letter

words

or

abbreviations

allowed

(such

as

DDT

or

TV),

then

the

minimum-letter

word-list

appears

to

be

nAB CoDE FiG

HIJacK

LiMN OP

QuRSh

TUrVes

WaXY

Zip

with

a

total

of

40

letters

used.

Each

of

the

26~

arrangements

of

the

alphabet

has

a

minimum

embedding:

there

is

some

list

of

words

with

a

total

of

n

letters,

but

no

list

of

words

with

n-l

or

fewer

letters

that

will

do

the

job.

What

are

the

maximum

and

minimum

values

of

n,

taken

over

all

possible

alphabetic

arrangements?

What

are

the

corresponding

ar-

rangements?

1t

is

quite

easy

to

find

the

minimum

value

of

n:

27.

There

is

no

pan

grammatic

word-list

based

on

the

Merriam-Webster

Pocket

Dictionary.

which

would

make

n

equal

to

26.

One

alphabetical

ar-

rangement

achieving

this

value

of

n

is

given

by:

LAMB

SQUaWK FJORD CHINTZ

VEX

GYP

1t

is

much

more

difficult

to

find

the

maximum

value

of

n.

After

considerable

trial

and

frror,

1

have

been

able

to

find

an

alpha-

betical

arrangement

for

which

the

minimum

word-list

has

52

letters:

Is

Up AgO

bEY

aCQuit

JaDe

oR

oX

GoWn PoeM

SaFe

He

LoNe

ZeBu

KiT

Vie

It

seems

wise

to

separate

the

vowels

and

consonants

and

treat

these

separately.

The

only

vowel-pairs

which

do

not

form

three-letter

words

in

the

Pocket

Dictionary

are

lU,

UI,

and

UA,

so

these

have

been

placed

together

to

form

1UA.

In

arranging

the

consonant-order,

one

must

a

void

consonant-pairs

that

form

three-letter

words

and

consonant-triples

that

form

five-letter

words;

this

has

been

accom-

plished

in

the

above

sequence

(PoeMS,

PraMS,

etc.,

are

not

bold-

face

entries).

There

are

a

few

letters

of

the

alphabet

(K,

Q,

C,

J,

V,

Z)

that

do

not

form

two-letter

words;

it

seems

advisable

to

place

these

near

each

other

if

possible,

or

at

the

end

of

the

se-

quence,

to

minimize

the

number

of

four-letter

words

they

can

form

with

their

immediate

neighbors.

In

the

sequence

above,

there

are

no

four-letter

words

containing

TV, CQ,

or

QJ.

146

Can

one

reduce

the

number

of

letters

to

51

or,

better

yet,

find

some

other

alpha

betica

1

arrangement

in

which

the

min

imum

number

of

letters

in

the

word-list

is

53

or

more?

This

seems

like

an

ideal

task

for

a

computer.

More

generally,

can

one

find

the

minimum

and

maximum

values

of

n

for

words

taken

from

other

'dictionaries?

The

larger

the

dic-

tionary,

the

smaller

these

values

will

be.

(For

all

but

the

smal-

lest

dictionaries,

the

minimum

value

of

n

will

be

26.)

For

a

final

problem,

consider

minimizing

the

number

of

words

in

the

list

instead

of

the

number

of

letters.

THE

DICTIONARY

OF

CONFUSABLE

WORDS

Written

by

the

eminent

lexicographer

Laurence

Urdang,

The

Dictionary

of

Confusable

Words

(Facts

on

File,

1988;

$29.ID

is

a

391-page

book

distinguishing

the

meanings

of

(1)

synonymic

groups

of

words,

such

as

strike/wildcat

strike/

sitdown

strike/slowdown

/work

to

rule/strike

action

(2)

words

that

are

spelled

or

sound

similar

even

though

not

synonymous,

such

as

affect/effect

or

compliment

/

com-

plement

(J)

members

of

a

highly-specific

group,

such

as

accordion

/

concertina

or

Old

Kingdom/Middle

Kingdom/New

Kingdom

or

judo/jujitsu/karate/kung

fu

Each

word

or

term

in

a

group

is

clearly

and

concisely

de-

fined;

especial

attention

is

given

to

the

differences

among

the

various

words

in

a

group.

Though

the

typical

discussion

is

half

a

page

or

less,

some

essays

extend

as

much

as

two

full

pages.

Although

much

of

the

same

ground

is

covered

by

Adrian

Room

in

his

books

Room's

Dictionary

of

Confusibles

(1979)

and

Room's

Dictionary

of

Dlstinguishables

71981),

there

is

surprisingly

little

overlap

between

Urdang

and

Room,

per-

haps

reflecting

the

idiosyncratic

nature

of

such

groupings.

Of

Urdang

1s

first

20

entries,

Room

duplicates

only

one

(accor-

dion/concertina)

and

approximates

another

(account

receivable/

account

payable

is

transmuted

into

the

more

general

account

/

bill

/

invoice/

statement).

Note

that

mere

spelling

varia

tions

are

not

considered

worthy

of

inclusion;

thus,

confusible/con-

fusable

is

not

an

entry!

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W~~bster

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about

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at

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that

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Stiffkey,

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much

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Great

Br

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Names.

The

May

198

detective

in

Vernon

MacI

was

really

:

in

The

Mov]

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partnE

of

Lew

Arcl

pa

rtner.

Darryl

Fran,

mercial

Atla

for

44

addil

to

add

to

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Zaca.

Zucke

Zella,

Zoro,

lA;

Zippel

~

Zodiac,

Zwal

Zanesville

N

Church

Stati<

SD;

Zach

TN;

Harry

Partri

Book

sounds

fFiat

Taro

al

taro,

Kinzab

to

me.

tI

The

Jeremy

Morse

ders

in

the

uses

a

11

the

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BOGY,