226
5-BY-5 LATIN NORD SQUARES
,
J A t
A L (
o
N
T
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W]
Y E
F R
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LEONARD GORDON
Tucson, Arizona
I S
T E
S T
To construct a Latin word square, make a word square out of
words with non-repeated letters and rank the letters in each
word by their alphabetic position (for example, ALICE==15423J.
If the ranking for horizontal words remains valid for the verti­
cal words, then the square is Latin. The concept of Latin word
squares was proposed by Dave Silverman in the August 1972 Kick­
shaws; in February 1973, Mary Youngquist and Murray Pearce
exhibited several 4-by-L; Latin word squares, and Mary exhibited
a 5-by-5 example with three invented but plausible II words".
In the Colloquy section of the February 1990 Word Ways, Frank
Rubin says "humans can be well-employed in following up leads
suggested by partial computer solutions". The following article il­
lustrates his point; 1 am surprised that more of this has not ap­
peared in Word Ways. However, partial computer results must be
deliberately developed in a form useful for human follow-up', and
the computer search must be fast enough to allow feedback and
multiple runs.
From my mixed list of 8779 five-letter words (principally Official
Scrabble Players Dictionary, but with additions from the Wordper­
fect Speller and Chambers Twentieth Century Dictionary), 1 extract­
ed 5875 words with five different letters. I then converted each
word to a sequence of five integers, each integer being eq ua 1 to
five times the letter-value (A = 0, B = 1, etc.) plus the rank.
For example, BLACK has the letter-rank 25134; B converts to 7 =
lx5 + 2, L 'converts to 60 = llx5 + 5, A converts to 1 = Ox5 + I,
C converts to 13 = 2x5 + 3, and K converts to 54 = 10x5 + 4. 1
then had the computer search for word squares based on this 130­
letter "alphabet". No additional testing was needed, although some
was useful for program speed. A two-letter 130x130 index is very
efficient, but a large computer memory is needed.
The first search yielded 34 word squares; in all of these ,_ the
horizontal and vertical word? match. All words can be found in
the OSPD with the exception of lDANT, IDOSE, ALOWE and CHIT A
(in Webster s Th ird) and HOTE I and HOTEN (in Webster s Second).
1
B 0 U R G
OUR I E
U R BAN
R I ANT
G E N T S
I
B0 UR G
OUR I E
U REA L
R I ANT
GEL T S
BRA V 0
R E WON
A W0 L S
VOL T E
o N SET
CAN T
A LOW
NOR I
T WI E
YEA R
Y
E
A
R
S
JAN T
A LOW
NOR I
T WI E
YEA R
Y
E
A
R
S
CAN T Y
A LOW E
NOR I A
L A ]
A U I
I D j
T I ~
H 0 1
C H
H
j
YI
A D ~
T R ]
S A 1
0 C 1
C L J
T A (
A R (
L Y
I 1
in t}­
two e
able
ARIMI
stert~
p I
I N
N A
A R
S M
A
corne
paira
ster I
My
letter
these
B 0
0 S
T WIG S
C H
YEA S T
K
A
S C
227
,
wt of
each
"423) .
ertiword
/(ick­
earce
ibited
Frank
leads
Le ilapt be
and
and
,
hcial
per:racteach
al to
rank.
I
7
=
+ 1,
4. I
130­
some
very
,
the
d in
:HlTA
~nd) .
y
E
A
S
T
J A N T Y
A L 0 W E
N 0 R I A
T W I G S
Y E A S T
D 0 I
T S
0 N S
I S T
T E L
S T E
E T
F R I T
R 0 S E
I S T L
T E L 0
S T E I
G R I T
R 0 S E
I S T L
T E L 0
S T E I
S
T
E
I
N
L A I T H
A U D I 0
I D A N T
T I N G E
H 0 T E N
C H A T S
H y D R A
A D M I T
T R I C E
S A T E M
0 C T A
e L A R
T A C 0
A R 0 S
L y S E
L
Y
S
E
D
S A I
A U D
I D A
T I N
H 0 T
L E
0 I
I N
D A T 0
A L E R
T E R A
0 R A T
S T I E
S
T
I
E
D
o
J A T
A L E R
T E R A
0 R A T
S T I E
S
T
I
E
D
S
I T E M S
T
E
I
T 0 R A H
E R U G 0
M A G 0 T
N
S H 0 T E
L E P T
L A I
P A R D
T I D A
A N I L
T H
L A I T H
A U D I 0
I D A N T
T I N G E
H 0 T E L
S A I T
A U D I
I D A N
T I N C
H 0 T E
S
M A.;N 0 R
A
A F 0 R E
R I A
N
0 R I E L
R E A L M
M E N S A
E Q u A L
N U D G E
S A G E R
A L E R T
Y 0 D L
oD E U
D E I T
L U T E
E M Y D
Y 0 D L
0 D I U
D I R T
L U T E
E M Y D
I 0
N T
G E
E N
G H A T
H Y D R
A D M I
T R I C
S A T E
T
E
M
C U B I T
U R E D 0
B E L 0 W
I D 0 S E
T 0 W E D
o
E
M
Y
D
S
E
A
N
I
L
E
H
0
T
E
L
E S C A R
S C 0 R E
C 0 S T A
A R T E L
R E A L S
B R I T
R 0 S E
I S T L
T E L 0
S T E I
L A I T H
A U D I 0
I D A N T
S A I T H
A U D I 0
I D A N T
T I
N G
E
T I
N G
S
T
E
I
N
E
H 0 T E I
H 0 T E I
C H A T S
H Y D R A
A D M I T
T R I B E
S A T E M
G H A T
H Y D R
A D M I
T R I B
S A T E
M E T
E A R
T R I
I T C
C H E
0 C
C H
T A
A R
L Y
I C
T H
C E
H S
S T
s
A
T
E
M
T A L
A R Y
C 0 S
0 S E
S E D
E
M
Y
D
S
1 1hen made a second search, forcing double Latin word squa res
in the top two rows and two left columns. and allowing one or
two errors elsewhere. A few promising squares emerged, and 1 was
able to repa ir one of them to a set of true double Latin squares.
AR lME, MAREW and LAWER are in the OED, and INULA is in Webster t s Th ird.
p I C U L
I N U L A
N A R E S
A R I M E
S M E A R
P I C U
I N U L
M A R E
A R I M
S M E A
L
A
S
E
R
P I C U L
I N U L A
M A T E y
A R I M E
S M E A R
P
I
M
A
S
I C
U
A R
R I
M E
N
U L
L A
E W
M E
A R
4 2 1
2 4 5
3 1 4
1 5 3
5 3 2
5 3
3 1
2 5
4 2
1 4
A third search which forced double squares in the lower right
corner and allowed errors in the upper left did not yield any re­
pairable squares. but identified a few more potentially useful Web­
ster's Third or OED words which 1 added to my list.
My fina 1 search used 8840 words of which 5936 had five different
letters; these produced SiX more 5-by-5 squares, given below. In
these, OSHAC and MUSHA are in Chambers, ARIME and ARlNE in
B 0 C K
0 S H A
C H I T
K A T E
S C A L
S
C
A
L
D
B
0
C
K
S
0 C K S
S H A
H I T
A T E
C A L
C
A
L
E
L I S
L I T H
I T H E
S H E 0
H E R L
A
H
E
R
L
S
G A M U T
A M U S E
M U S H A
U S H E R
T E A R Y
S C R A N
C L A R 0
R A G I S
A R I M
N 0 S E
E
D
S C R
C L A
R A G
A R I
N 0 S
A N
R 0
I S
E
E D
N
228
LE
the OED, and SCRAN, ALlSH, and KATEL in Webster's Second.
Although I was not hopeful, my success with five-letter words
prompted me to look as six-letter words. Restricting the search
to simple squares made the process easy. As expected, the results
were negative.
FRP
IS THIS QUESTION RHETORICAL?
Tor
Pop grammarians such as William Safire, wincIng when Presi­
dent Bush confuses lay T.-lith lie, inveigh against misuses of
p
the English language. But for Joe Citizen, reading a book
lett
on the do 's and don 't's of grammar IS about as exciting
ter
as kissing his sister or clean ing the garage. Can grammar
MUI
be made fun, or at least more palatable?
I
Canadian computer programmer and language aficionado Jon
the
Steeves has answered this by inventing and marketing the
wil
game of Moot, a painless way to learn about the meanings
lett
and usages of words, not by solitary dictionary lookup, but
del,
by discussion among peers. Specifically, it consists of a thou­
the
sand questions like
cas
charlatan falsely claims to a) be someone b) know some­
thing
- what movie title would be Magus Ozianus in Latin?
- bus was coined from what three-syllable T,./ord?
- is the word ineffable ineffable?
-
a
One question begins "The natives want to lay down and rest .."
Et tu, Steeves?
twi.
p
wa~
del,
wor
mor
apf
I (
spa
er
The game can be played either as a form of solitaire in T.-Ihich
tr.-.'o to five players discuss each question and jointly arrive
at the most plausible answer, or as a two-team effort in which
1
Team A jointly arrives at an anST.-;er which Team B is allowed
ety
to challenge with an ansl..;er of their own. Colloquy forms
Lll\
the soul of the game: it forces one to refine one's ill-formu­
tra
lated ideas In the face of overlooked evidence. Ob viously,
TLI
the game 1.lorks best in a group l..;ith similar ba ckgrounds
is
(say, co-r.-./orkers or college graduates). It should appeal to
the
the Word Ways subscriber, but is hopelessly cerebral for the
not
high-school dropout.
Questions are divided into four groups according to level
of difficulty, but I found little difference among them. The
game T.-/ould be more interesting if there existed strategies
for maximizing one's score (number of correct answers, scaled
by difficulty),. one determines wha t level must be answered
by the roll of a 12-sided die. Steeves loves wordplay
("is a
pale-complexioned Mexican wan?"). Many questions distinguish
between closely-related words (blase-jaded, enormity-atrocity).
The game is available for $40.95 from the author (Moot,
337 W Pender, Vancouver V6B lT3 Canada).
fou
eXI
ma
I
bU1
kn<
so
A
204­
B
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