248
WORD NETWORKS ON WORDLOCKTM
A. ROSS ECKLER
Morristown, New Jersey
-
Wordlock™, a combination lock using words instead
of
numbers, was created by Todd Basche, a
Silicon Valley executive. Sold by Staples for $5.98 (in blue
or
black)
or
$3.90 (in orange),
it
consists
of
five independently-rotating rings, yielding one hundred thousand different positions,
anyone
of
which the user can select. Because words are more easily remembered than numbers,
he inscribed four
of
the rings with ten different letters each, and the fifth with nine different
letters and a blank, allowing the user to pick either a four-letter or a five-letter word (left column):
MA
T C
H M
A
S
0 N
J 0
C
S
S
J U N T
A
L E I N
L
0
C I
S
L E E K S
T A L E
A I S Y L
A L L A Y
C
H 0 A 0 C
H
I
N K
0 U L L
Y
0
I
T C H
B
RA
I N B E R Y L
E N R T
A E N 0 E 0
T T N 0 E T R
E S S
With the default factory setting (left column), four
of
the ten combinations can be simultaneously
read
off
as words. Three
of
these, MATCH, BRAIN, and SLEEK, must have been deliberately
created to reside on
the
three raised sections
of
the rings, but DULLY was probably an
afterthought. However, Basche could have rearranged the non-raised letters
on
the rings to spell
TfllNE (or TENSE), ENROL, CODAS and LIST, for a total
of
seven out
often
words.
Rearranging all the lett
er
s on the rings, could Basche have created a full ten words? In other
words, can ten
mutually non-crashing words be found which use the specified letters on the
various rings? (Two words are non-crashing
if
they have no common letters
in
the same position,
such as sTraw and oTher
or
hoUse and brUnt.) The answer
is
yes ten words from the Merriam-
Webster Pocket Dictionary are given
in
the right column above. More generally, a set
of
seventeen mutually non-crashing Pocket Dictionary words can be found on page
211
of
the
author
's
book Making the Alphabet Dance.
Ba
sche apparently consulted letter-frequency tables to select the letters on the rings. Th
commonest ten first letters for four-letter words in the
Pocket Dictionary are SBPTCLDMFR, and
for
fi
ve-letter ones, SCBAPTFGMD--so why did he select J and E for the first ring in preferen e
to
P and
F?
In
the fourth ring, Y
is
rarely found in five-letter words and
is
less common than nin
other letters (SETLDKNMR) ending four-letter ones; R would have been a better choi
e.
Th t P
ten
Pocket Dictionary I,etters terminating five-letter words are EYTRDLNHKS but h I
included S
in
his set
of
nine because
of
noun plurals and verb present tenses. Howe r h
Id
have substituted T for
the
relatively rare
A,
and (possibly) R for H or K.
The most interesting wordplay possibility for Wordlock™
is
found
in
the ord ladd r th
successive transformation
of
one word into another by changing a single I
tt
r (i
..
b tating a
249
single ring). The thousand-plus Pocket Dictionary words present
on
the rings
of
the lock can
be
sorted into various word networks,
in
which any word
can
be converted to any other word
by
successive single-letter changes.
It
is
remarkable that more than
90
per cent
of
all
possible words
lie
in
a single network;
in
fact, the largest network not connected to the main network consists
of
only six words! The five-letter part
of
the
main
network
is
displayed
in
sections
at
the end
of
this
article, with
all
connections to the four-letter part
of
the network (too tangled to diagram) shown.
In
theory, any word
in
the main network
can
be
transformed to a word with different letters
in
every position
in
a maximum
of
five steps (such as crane-crank-crack-crick-click-slick). The
reality
is
that many more steps are usually needed. Consider,
for
example, CHlLD to MlRTH.
The shortest connection
is
apparently
25
steps:
CHILD-chi
II-shi
II-sti
II-stall-stal k -stank -shank -thank -than-that -teat -test -lest -Iast-mast-
mart-Mars-marsh-march-match-batch-bitch-birch-birth-MfRTH
Can
it
be
done
in
24 or fewer steps? More important, can one locate another pair
of
words
for
which the shortest possible connection
is
greater than 25? Each pair
of
words
in
the network
has
a
shortest-possible-connection number; the largest such number for any pair
of
words
in
the
network
is
called the span
of
the network.
The four-letter part
of
the main network contains the densest cluster
of
words. This is evinced by
the fact that the span
of
the four-letter network appears to
be
only
10,
as
given for example
by
-du
Iy
-du
II-do
11-
mo
II-mo
It
-moat -coat -chat
-ch
it-
ruLY
crnc
-jury-bury-burn-turn-tern-teen-then-thin-chin-
Note that
DUTY to
crnc
has the same span.
Interestingly, only four
of
the
ten
non-crashing words presented earlier are
in
the main network.
A typical connection (not necessarily the shortest)
is
CHINK
-c
link
-sl
ink
-stink -stick -stack-stalk-STALE
ST ALE-state-slate-slat-seat-meat-melt-malt-mart-Mars-marsh-march-match-batch-bitch-DITCH
DITCH-bitch-batch-match-march-marsh-Mars-mart-mare-tare-tarn-tern-teen-then-thee-tree-trees-
TRESS
LOCO
is
connected only with LOCI,
and
ALLAY with ALLOY -ALLEY -ALLAH; the other four
are isolanos (i.e., have
no
connecting words
in
the Pocket Dictionary).
THREE
is
the only cardinal, TENTH
and
NINTH the only ordinals, BORON the only element,
MAINE the only state, and ARIES the only
sign
of
the Zodiac. However, there exist three out
of
the twelve months, MARCH, JUNE and JULY, which are connectable. How about connecting
CHINA, CHILE and MALTA (which have one-step connections to words
in
the network)? Or
opposites such
as
TrnCK and
nON
(an easy one-step via THINK), or EARLY
and
LATE? Alas,
one cannot connect BLESS
and
CURSE, DIRTY
and
CLEAN, SATAN and ALLAH, or BIRTH
and DEATH!
•
250
Partially-capitalized words connect with the four-letter network
Boldface words transfer five-letter words
in
the first network to five-letter words
in
the second
When three words are joined by equal signs, one can
go
directly from word I to word 3
When three vertical words are separated by underlines, one can go directly from word 1 to word 3
stein-stain-slain
staid
blain
trail
SHINy THINe-
THANk
brain=drain=train
SHINe-THINe
braid
seine
I
briny
BRANd-BRANs-BRASs
I I I
BRAYs
I
brace
trine-trite
brine
blank-b
land
BRATs
I
I I I I I I
trace-trice
drink-brink-
blink
-blind
BRASh
-
track-trick-------bri
ck
I
crash-clash-slash
I
brisk
blend-bleed
crass-class
I I
cress-------chess
thick
I
tress-dress
I
bleak
dread
I I
CHICk
break-bread------
-breed
I
dries-dried
check
creak
tread=trend=TREEd
-TREEs=tries=tried
cheek-------creek---I
---------creed
triad
creel
trial
cries-cried
Aries
ARIAs-alias
drill-trill
array-arras
drily
daily-DAISy
dally=======DULLY=======DOLLy
manly
I I
JELLy-jolly
EARLy-MARLy-madly I BILLy=BULLy=BELLy
badly
TALLy
I I
BELLe-belie
sadly-sally=SILLy=sully
SALTy-SILTy-surly=CURLy=burly
Malay-MALTy
crate-crane
THINk
crank-
crack
-
crick
---
CHINk-CHINa
CLANk-clack-
click---clink
black
I I
slack-slick---slink
snack
Islice
I
shank
-shack
I I
stand-stank
-sta
ck-stick--
-stink
I
scaly-scald
I
scale
I
shale---I---shall-shell
state-stale=stalk=stall
I
SLATe
stile-------still-shill
elate----
---elite
chill-child
Transfers
black
to
blank
shank
to
thank
think
to
thank
think
to
thick
think
to
thine
chink
to
chick
click
to
chick
crick
to
chick
crick
to
trick
crack
to
track
clink
to
blink
251
milch
mulch
lunch
=
bunch
=
munch
lurch
I
beech-leech
larch
bench
=
belch
=
beach=leach=teach
MARSh-march
LEASh
match
=
catch=batch
LEASe=cease
=TEASe
bitch-ditch
chase
birch
mirth-birth
berth
metal-medal-modal-MODEl-MOTEl
I
coral-moral-mural
canal-banal-basal-basil
basin
basis
BASEs
steed-steel
stead
I
steak-steal
sneak
baste
=
CASTe=taste-tasty-TESTy
CONEy-money
mosey
MASSy=MOSSy=MESSy=MUSSy
sassy
BOSSy MUSTy-MISTy-MINTy
•
SlSSY
LUSTy
Allah-allay=alley=alloy
moron-boron-baron=baton=bacon
sense=dense=tense-terse
decal-decay-decoy
delay
Note that the steed network
is
the largest one not connected with the main network.
