A Survey of Small Squares

Word Ways, Dec 975

In a desperate attempt to make ever-larger word squares, logologists have succeeded only in producing monsters such as the ten-by-ten tautonymic word squares featured in the August and November 1973 issues of Word Ways. Is it not time to recall the intrinsic beauty and extreme versatility of smaller word squares -- say, those of size six-by-six or less? This article surveys a wide variety of such squares, taken from past issues of Word Ways, from Dmitri Borgmann's Language on Vacation (Scribner's, 1965), and from Martin Gardner's Mathematical Games column in Scientific American.

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A Survey of Small Squares

MAXE Y BROOKE Sweeny. Texas In a desperate attempt to make ever-larger word squares I logologists have succeeded only in producing monsters such as the ten- by-ten tautonymic word squares featured in the August and Novem.ber 1973 issues of Word Ways. Is it not time to recall the intrinsic beauty and extreme versatility of smaller word squares -- say, those of size six-bysix or less? This article surveys a wide variety of such squares. taken from past issues of Word Ways. from Dmitri Borgmann! s Language on Vacation (Scribner! s. 1965), and from Martin Gardner ' s Mathematical Game s column in Scientific American. - A SURVEY OF SMALL SQUARES A p A R T P E W E E A W A R E R E R A N T E E N S E W E W A R E R A A In a progressive word square, the first letter of a word is deleted and another letter is added at the end CAR 0 M to pr oduc e the next war din the s quar e . A ROM A ATE The five - by - five example at the right ROM A N TEA has been taken from Language on Va­ o MAN I EAT tion. The cyclic square is a special MAN I C case of a progressive word square -­ in it, each word is formed by placing the first letter of the preceding word at the end. A three-by-three example consisting of very common words is given at the ·right. In the August 1972 Word Ways. ERR E c Y S T Mary Youngquist presented a [our­ SEE R o P A H by-four double word square using S ERE RIM U only th ree diffe rent lette r s. On the ESE R F LED other hand, George H. Rope s of Scarsdale, N. Y. successfully constructed a four-by-four double word square using sixteen different letters. None of his words were plurals or proper names, and all can be found in Webste r I s Second. This tour de force was originally printed in the July/August issue of the WT Technology Review. and was cited in the November 1974 War d Ways. In sequential word squares, .a given word is successively placed in each position of a square. For example, the word square sometimes FALLS down F A L L S A F A C E B E F I T A R E A L FA L L S E V A D E L E A V E A L L o T F ALL S L A V E D C L 0 S E I D L·E S S L E D S E S T E R T E S S A C RO F T R A D A R ODD L Y F A L L S TRY S T S T A F F TE R R A AR E A L FR A I L FA L L S but it always RISES again. M A. N o R S C A R P A L I B I C U R 1.0 N I M E S A R I S E o B E S E R I S E S R I S E S P 0 E S Y V E R S T E L I T E R I S E S S T E P S T E S S A ORAGE R I S E S A S SET GEE S E E S T E R R I S E S I DO L A S o R E L ELEM I SAL I X On page III of Language on Vacation, Dmitri Borgmann exhibited several three- by-three double word squares in which the nine L A C P A L P A R letter s. read off in order. form E R A A V E A P A a word of their own. T E D R E D T E D In the same book, he defined the sentential word square -- one in which the component words, read off in order, make some sort of sense: LEAVE ELLEN ALONE, VENOM ENEMY. J. A. Lindon pre­ sented more than 100 five-word sentences of this type in the Novem­ ber 1969 Word Ways. 1£ the word square is reversible, the resulting sentence will be palindromic -- but now it is best to relax the require­ ment that th square: RK In The 1968 under lenged his r containing 5 rever sals, he was able at the left b encouraged squares (gi squares we Harold Johr GET A I A SUP In the F proposed th n different way that ea row and co] ial case of word squar able squarE tie sand Cu Latin both wise) , ME' English wo In the ed the unus the right. the classic; entries are is a Latin! ther than a each of the ly. assign' from one t( numerical, square in n in the abov' row, exact: the whole h square. In the six- byATE TEA EAT preceding ery common :: Y S T J P A H RIM U F LED ouble word ilere plurals l. This tour the MIT ord Ways. :ly placed in 30metime s r A F F ~ R R A tEA L t A I L ~ L L S [ S E S ) 0 L A ) R E L oJ E M r \ L I X exhibited PAR A P A TED -- one in ;ort of ndon pre­ . Novem­ resulting le require­ ment that the words of the sentence match the words in the word square: REVEL EVER, EVE! 0 EVE, REVEL EVER! In The World I s Best Puzzles (1925). reprinted by Scribner' s in 1968 under the title 300 Best Word Puzzles, Henry E. Dudeney chal­ lenged his readers to construct a three-by-three double word square containing sixteen different words: the six standa-rd words, their six r eve r sals. the two diagonal words. and their two reve r sal s. The best he was able to achieve was a square containing thirteen words, given at the left below. Martin Gardner in the June 1964 Scientific American encouraged his readers to do better, and in October he cited five squares (given below) in which all sixteen words were placed. The se squares were contributed by Dmitri Borgmann, Leslie Card, Mr s. D. Harold Johnson, Peter Kugel and Wyile Wilson, respectively. GET A I A SUP ATE RAE TOR ERA LEE SAN A T S R I A TAD S E R TAO A R D EEL TAO ART In the February 1964 issue of Scientific American, Solomon Golomb proposed the name Latin word square for an n- by-n word square using n dif (...truncated)


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Maxey Brooke. A Survey of Small Squares, Word Ways, 975, Volume 8, Issue 2,