W A S S A I L R A C I S M C H A P S B L O C
A N T E N N A E V I N C E H O U R I R U D Y
S T R I N G Y P E R S O N A R R A S A X I S
S E I Z U R E A S C E N T M A I N S G E N T
A N N U L A R S T U C C O P E C K Y (5)
I N G R A T E T A S T E R (2)
L A Y E R E D (113)
(54)
These examples represent four classes of “M-W squares”, word squares that can be made from headwords in the 5th edition of the Merriam-Webster Collegiate Dictionary, including the appendices of boys' and girls' names. Inflected forms, such as plurals, are excluded unless they literally appear in the dictionary (typically for irregular or multiple inflected forms). The classes, whose sizes are given above, are
7×7 squares
6×6 double squares (different words across and down)
5×5 double squares with extra words on the diagnoals
4×4 motley squares (double squares, all letters different)
The displayed 7×7 and 6×6 squares were pronounced best in class by the nonpareil word gamester Dmitri Borgmann. [A. Ross Eckler, Language on Vacation St. Martin (1995)]
Each class is exemplified by a square of the largest size that meets the class criterion. There are thousands of M-W squares smaller than 7×7, but none larger. Double word squares are far less common: The number of n×n double squares is comparable to the number of n+1×n+1 unrestricted squares. [Chris Long, Mathematics of square construction] The biggest M-W double word squares are 6×6s.
The 5×5 is a rare find. Only two out of the 529,286 double squares of this size bear words on both diagonals. The two differ in just one letter—either A or I in the middle of PR_NK. Not surprisingly, these trophies found in the bottom of a very deep barrel are flush with uncommon words: :
ARRAS tapestry ARRIS sharp edge where surfaces meet, as in moldings HORAE Greek goddesses of seasons HOURI companion maiden in Muslim paradise PARRS (plural) young salmon or trout PECKY marked with fungal decay, spalted PRINK primp
Enumerating word squares was a big deal when I first did it in the 1970s. The search for 7×7s sopped up spare hours on a PDP-11 computer over more than two months. Now a laptop can do the job in minutes. A version of the C program for the search is available here. Much word square lore, including more squares of mine, can be found in Word Ways, an open-access publication with a good search facility.
Two more squares can be made by replacing single letters in the middle square so thatB A C H B L O C N A G S O I L Y R U D Y E C R U G R U M A X I S W H I M S T E N G E N T T Y P O
BLOC/BRAG become FLOC/FRAG, or
BRAG/GENT become BRAW/WENT
AMASSER AMASSER APPOINT APPOINT APPROVE MELKITE MELKITE PRANCER PRANCER PURANIC ALRIGHT ALRIGHT PALETTE PALETTE PREBEND SKINNER SKINNER ONENESS ONENESS RABBITY SIGNORA SIGNORA ICTERUS ICTERUS ONEIDAS ETHERIC ETHERIC NETSUKE NETSUKE VINTAGE RETRACE RETRACT TRESSED TRESSEL ECDYSES ASCESIS ATTEMPT BLESSED BLESSED BLESSED STAMINA TUATARA LUNETTE LUNETTE LYNETTE CAPELIN TANAGER ENTREAT ENTREAT ENTREAT EMERITI ETATIST SERIATE SERRATE SERIATE SILICIC MAGICAL STEARIN STEARIN STEARIN INITIAL PRESAGE ETATIST ETATIST ETATIST SANICLE TARTLET DETENTE DETENTE DETENTE BLESSED BRISTLE CASSAVA CASSOCK CASSOCK LYNETTE RENEWAL ASHERIM AZTECAN AZTECAN ENTREAT INCLINE SHARRON STYRENE STYRENE SERRATE SELFDOM SERVILE SERIATE SERRATE STEARIN TWIDDLE ARRISES OCEANIC OCEANIC ETATIST LANOLIN VIOLENT CANTINA CANTINA DETENTE ELEMENT AMNESTY KNEECAP KNEECAP CASTOFF CATALPA CELESTA CELESTA CELESTA APPAREL AIRMAIL ENACTOR EXACTER EXACTER SPICILY TRIPOLI LABORED LAWLESS LAWLESS TACTFUL AMPUTEE ECOTONE ECLIPSE ELLIPSE ORIFICE LAOTIAN STROMAL STEPHEN STEPHEN FELUCCA PILEATE TOENAIL TESSERA TESSERA FLYLEAF ALIENEE ARDELLE ARSENAL ARSENAL CELESTA CELESTA CELESTA CESSPIT CHASSED EXACTOR EXALTER EXALTER ESTUARY HECTARE LABORED LAWLESS LAWLESS STELLAR ACHATES ECOTONE ECLIPSE ELLIPSE SULTANA STATICS STROMAL STEPHEN STEPHEN PALADIN SATIATE TOENAIL TESSERA TESSERA IRANIAN ERECTOR ARDELLE ARSENAL ARSENAL TYRANNY DESSERT CONTEND CONTENT DERIVER ESCOLAR FACTICE OVERSEA OVERSEA ERUDITE SCALENE AURORAL NEGATON NEGATON RUPIAHS CAPITAL CREMATE TRACING TRACING IDIOTIC OLIVINE TOMENTA ESTIVAL ESTIVAL VIATICA LETITIA IRANIAN NEONATE NEONATE ETHICAL ANANIAS CATTALO DANGLER TANGLED RESCALE RELEASE ELEANOR FARTHER FESTIVE FRESCOS GRISTLE HASSOCK ACEROSE ETHANOL RESTART RENEWAL AZTECAN REMORSE SHINGLE ESTELLE INCLINE STYRENE TROMMEL TANTRUM STELLAR SELFDOM SERIATE HORMONE INGRATE CALLANT TWIDDLE OCEANIC ESSENIC VOLUTIN ORLANDO LANOLIN CANTINA REELECT ELEMENT STERTOR ELEMENT KNEECAP HASSOCK HATCHET HATCHET JACKLEG LATCHET AZTECAN ARRAYER ARRAYER ATHLETE ARRAYER STYRENE TRINDLE TRUNDLE CHEATER TRINDLE SERRATE CANTALA CANTALA KLANISM CANTALA OCEANIC HYDATID HYDATID LETITIA HYDATID CANTINA EELLIKE EELLIKE ETESIAN EELLIKE KNEECAP TREADER TREADER GERMANE TREADER LATCHET LEACHER NORTHER RATCHET RATCHET ARRAYER ESTHETE OPEROSE ARRAYER ARRAYER TRUNDLE ATTACHE REMORSE TRINDLE TRUNDLE CANTALA CHATTEL TROMMEL CANTALA CANTALA HYDATID HECTARE HORMONE HYDATID HYDATID EELLIKE ETHERIC ESSENIC EELLIKE EELLIKE TREADER REELECT REELECT TREADER TREADER REACHER RESTIVE SETBACK TEACHER TOBACCO ESTHETE ETHANOL ETHANOL ESTHETE OVERALL ATTACHE SHINGLE THISTLE ATTACHE BEVELED CHATTEL TANTRUM BASTILE CHATTEL AREOLAS HECTARE INGRATE ANTIGEN HECTARE CALLANT ETHERIC VOLUTIN COLLEGE ETHERIC CLEANSE REELECT ELEMENT KLEENEX REELECT OLDSTER TRESTLE VIRAGOS WASSAIL WETBACK WRESTLE RENEWAL INEXACT ANTENNA ETHANOL RENEWAL ENPLANE REVILER STRINGY THISTLE ENPLANE SELFDOM AXILLAE SEIZURE BASTILE SELFDOM TWADDLE GALLANT ANNULAR ANTIGEN TWADDLE LANOLIN OCEANIC INGRATE COLLEGE LANOLIN ELEMENT STRETCH LAYERED KLEENEX ELEMENT