mmar@sphinx.UChicago.UUCP (Mitchell Marks) (08/20/85)
Note: The following began as a response to an inquiry in net.nlang about
the Latin word square. After giving some miscellaneous examples and discussion
I got tired of trying to type these in accurately, and left the last few
as problems -- hence the posting here. The puzzles, set partway through,
are as follows:
1. A 6 x 6 x 6 symmetrical English word cube.
2. A 6 x 6 x 6 non-symmetrical English word cube.
3. A 7 x 7 x 7 symmetrical English word cube.
Word-admissibility criteria are up to you: the stricter you are, the happier
you will be with your solutions. The discussion below doesn't define
"word cube", but it's the obvious 3D extension of a word square. The examples
given in the reference cited below present the cubes as numbered squares,
each representing one layer.
The remainder of this posting is the same as that in net.nlang.
S A T O R
A R E P O
T E N E T
O P E R A
R O T A S
This is more than a palindrome, it's a word square. (Indeed, it's
not very palindromic -- only TENET is reversible by itself.) This
was found as an inscription and, so far as I know, its authenticity
has never been challenged. If authentic, it's the earliest known
example.
Martin Gardner discussed word squares a few times, but I can't
put my finger on specific comments about this one in any of the collections
of his I have. So the remainder of this paragraph is based on possibly
inaccurate memory. Attempts have been made to construe it as a coherent
sentence, but it seems to be obscure. The problem is a word or two that
doesn't occur anywhere else in Latin. Taking the problem word as a
proper name (I think it was AREPO), one translation was "The farmer Arepo
holds the wheel at work".
One reference on word squares that I do have at hand is _Word_
_Recreations_from_Word_Ways by A. ross Eckler (Dover #23854-7, 1979).
Though the book is under a 1979 copyright, original serial publication
of some of the material goes back to 1969, so comments on records
and state of the art are probably out of date. Eckler distinguishes
`regular word squares', like the Latin one, in which the same words are
used horizontally and vertically, from `double word squares', in which
the sets of horizontal and vertical words are disjoint.
The best pre-1976 6x6 double square was the following from
Dmitri Borgmann:
SAPPER
ADIATE
MARTHA
UNITER
ECTENE
LEERED
In 1976 M. D. McIlroy made a computer survey for 6 x 6 squares at
Bell Labs. He came up with 117 different squares, most of which were
less dependent on rare or obscure words than the above, including
several in which 11 out of the twelve words could be found in Webster's
Pocket Dictionary. Some of them come in families involving minor
substitutions, but others remain singlets. Picking one at random
from those Eckler lists:
P R I M A L
R E C I P E
O T I T I S
S E C R E T
E N L A C E
R E E L E R
Frank Rubin of Wappingers Falls NY made a computer search for a
10 x 10 square, using a list of 35,000 words from Webster's Second
Unabridged (Eckler doesn't say when this was). He didn't find one.
His best result was a square in which the last two columns and
rows were not filled with real words:
A C C O M P L I S H
C O O P E R A N C Y
C O P A T E N T E E
O P A L E S C E N T
M E T E N T E R O N
P R E S T A T I O N
L A N C E T O O T H
I N T E R I O R L Y
S C E N O O T L
H Y E T N N H Y
In 1976 Paul Remley proposed the problem of a 6x6x6 word cube, and
the author (it seems to be Eckler) says he constructed one in a
few hours, using the OED as his word list. He also constructed a
non-symmetrical 6x6x6 cube, relaxing the criteria for words somewhat.
He also provides a 7x7x7 symmetrical cube. Rather than listing them,
I'll cross-post this to net.puzzle, and see what people can come up
with.
As a guide to the level of stringency or laxity involved, here
are the questionable words Eckler had to allow himself:
For the 6x6x6 symmetrical: all in OED.
For the 6x6x6 non-symmetrical: 82 of the 108 from OED, or
inferred from OED. 5 from Webster's Third. 4 from English Dialect
Dictionary. 2 foreign words. 3 place names from Webster's New
Geographical Dictionary. The remaining 12 include `inferred terms'
like REPERE and ANT-EGS, two-word forms like HE MENT (archaic past of mend),
and citation-form plurals like SWESH'S.
For the 7x7x7 symmetrical, oddities include ARREESTS, ELAATER,
EMERYES, GYANTER, ILLECTE, NAYANTE, NIBLICS, SERRITA, SLASTER, SSSSSSS,
STEININ', TELMEST, TINTILY, and TUTELLE.
Wait! It's not Eckler, it's Jeff Grant.
--
-- Mitch Marks @ UChicago
...ihnp4!gargoyle!sphinx!mmar
--
-- Mitch Marks @ UChicago
...ihnp4!gargoyle!sphinx!mmar