From Wikipedia, the free encyclopedia
A word square is a type of acrostic. It consists of a set of words written out in a square grid, such that the same words can be read both horizontally and vertically. The number of words, which is equal to the number of letters in each word, is known as the «order» of the square. For example, this is an order 5 square:
| H E A R T |
| E M B E R |
| A B U S E |
| R E S I N |
| T R E N D |
A popular puzzle dating well into ancient times, the word square is sometimes compared to the numerical magic square, though apart from the fact that both use square grids there is no real connection between the two.
Early history[edit]
Sator Square[edit]
The first-century Sator Square is a Latin word square, which the Encyclopedia Britannica called «the most familiar lettered square in the Western world».[2]
Its canonical form reads as follows:
| 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 |
In addition to satisfying the basic properties of word squares, it is palindromic; it can be read as a 25-letter palindromic sentence (of an obscure meaning) and it is speculated that it includes several additional hidden words such as reference to the Christian Paternoster prayer, and hidden symbols such as the cross formed by the horizontal and vertical palindromic word «Tenet». The square became a powerful religious and magical symbol in medieval times, and despite over a century of considerable academic study, its origin and meaning are still a source of debate.[3][4]
Abramelin the Mage[edit]
If the «words» in a word square need not be true words, arbitrarily large squares of pronounceable combinations can be constructed. The following 12×12 array of letters appears in a Hebrew manuscript of The Book of the Sacred Magic of Abramelin the Mage of 1458, said to have been «given by God, and bequeathed by Abraham». An English edition appeared in 1898. This is square 7 of Chapter IX of the Third Book, which is full of incomplete and complete «squares».
| I S I C H A D A M I O N |
| S E R R A R E P I N T O |
| I R A A S I M E L E I S |
| C R A T I B A R I N S I |
| H A S I N A S U O T I R |
| A R I B A T I N T I R A |
| D E M A S I C O A N O C |
| A P E R U N O I B E M I |
| M I L I O T A B U L E L |
| I N E N T I N E L E L A |
| O T I S I R O M E L I R |
| N O S I R A C I L A R I |
No source or explanation is given for any of the «words», so this square does not meet the standards for legitimate word squares. Modern research indicates that a 12-square would be essentially impossible to construct from indexed words and phrases, even using a large number of languages. However, equally large English-language squares consisting of arbitrary phrases containing dictionary words are relatively easy to construct; they too are not considered true word squares, but they have been published in The Enigma and other puzzle magazines as «Something Different» squares.
Modern English squares[edit]
A specimen of the order-six square (or 6-square) was first published in English in 1859; the 7-square in 1877; the 8-square in 1884; and the 9-square in 1897.[5]
Here are examples of English word squares up to order eight:
| A | N O | B I T | C A R D | H E A R T | G A R T E R | B R A V A D O | L A T E R A L S |
| O N | I C E | A R E A | E M B E R | A V E R S E | R E N A M E D | A X O N E M A L | |
| T E N | R E A R | A B U S E | R E C I T E | A N A L O G Y | T O E P L A T E | ||
| D A R T | R E S I N | T R I B A L | V A L U E R S | E N P L A N E D | |||
| T R E N D | E S T A T E | A M O E B A S | R E L A N D E D | ||||
| R E E L E D | D E G R A D E | A M A N D I N E | |||||
| O D Y S S E Y | L A T E E N E R | ||||||
| S L E D D E R S |
The following is one of several «perfect» nine-squares in English (all words in major dictionaries, uncapitalized, and unpunctuated):[6]
| A C H A L A S I A |
| C R E N I D E N S |
| H E X A N D R I C |
| A N A B O L I T E |
| L I N O L E N I N |
| A D D L E H E A D |
| S E R I N E T T E |
| I N I T I A T O R |
| A S C E N D E R S |
Order 10 squares[edit]
A 10-square is naturally much harder to find, and a «perfect» 10-square in English has been hunted since 1897.[5] It has been called the Holy Grail of logology.
Various methods have produced partial results to the 10-square problem:
- Tautonyms
Since 1921, 10-squares have been constructed from reduplicated words and phrases like «Alala! Alala!» (a reduplicated Greek interjection). Each such square contains five words appearing twice, which in effect constitutes four identical 5-squares. Darryl Francis and Dmitri Borgmann succeeded in using near-tautonyms (second- and third-order reduplication) to employ seven different entries by pairing «orangutang» with «urangutang» and «ranga-ranga» with «tanga-tanga», as follows:[7]
| O R A N G U T A N G |
| R A N G A R A N G A |
| A N D O L A N D O L |
| N G O T A N G O T A |
| G A L A N G A L A N |
| U R A N G U T A N G |
| T A N G A T A N G A |
| A N D O L A N D O L |
| N G O T A N G O T A |
| G A L A N G A L A N |
However, «word researchers have always regarded the tautonymic ten-square as an unsatisfactory solution to the problem.»[5]
- 80% solution
In 1976, Frank Rubin produced an incomplete ten-square containing two nonsense phrases at the top and eight dictionary words. If two words could be found containing the patterns «SCENOOTL» and «HYETNNHY», this would become a complete ten-square.
- Constructed vocabulary
From the 1970s, Jeff Grant had a long history of producing well-built squares; concentrating on the ten-square from 1982 to 1985, he produced the first three traditional ten-squares by relying on reasonable coinages such as «Sol Springs» (various extant people named Sol Spring) and «ses tunnels» (French for «its tunnels»). His continuing work produced one of the best of this genre, making use of «impolarity» (found on the Internet) and the plural of «Tony Nader» (found in the white pages), as well as words verified in more traditional references:
| D I S T A L I S E D |
| I M P O L A R I T Y |
| S P I N A C I N E S |
| T O N Y N A D E R S |
| A L A N B R O W N E |
| L A C A R O L I N A |
| I R I D O L I N E S |
| S I N E W I N E S S |
| E T E R N N E S S E |
| D Y S S E A S S E S |
- Personal names
By combining common first and last names and verifying the results in white-pages listings, Steve Root of Westboro, Massachusetts, was able to document the existence of all ten names below (total number of people found is listed after each line):
| L E O W A D D E L L 1 |
| E M M A N E E L E Y 1 |
| O M A R G A L V A N 5 |
| W A R R E N L I N D 9 |
| A N G E L H A N N A 2 |
| D E A N H O P P E R 10+ |
| D E L L A P O O L E 3 |
| E L V I N P O O L E 3 |
| L E A N N E L L I S 3 |
| L Y N D A R E E S E 5 |
- Geographic names
Around 2000, Rex Gooch of Letchworth, England, analyzed available wordlists and computing requirements and compiled one or two hundred specialized dictionaries and indexes to provide a reasonably strong vocabulary. The largest source was the United States Board on Geographic Names National Imagery and Mapping Agency. In Word Ways in August and November 2002, he published several squares found in this wordlist. The square below has been held by some word square experts as essentially solving the 10-square problem (Daily Mail, The Times), while others anticipate higher-quality 10-squares in the future.[5][8]
| D E S C E N D A N T |
| E C H E N E I D A E |
| S H O R T C O A T S |
| C E R B E R U L U S |
| E N T E R O M E R E |
| N E C R O L A T E R |
| D I O U M A B A N A |
| A D A L E T A B A T |
| N A T U R E N A M E |
| T E S S E R A T E D |
There are a few «imperfections»: «Echeneidae» is capitalized, «Dioumabana» and «Adaletabat» are places (in Guinea and Turkey respectively), and «nature-name» is hyphenated.
Many new large word squares and new species[clarification needed] have arisen recently. However, modern combinatorics has demonstrated why the 10-square has taken so long to find, and why 11-squares are extremely unlikely to be constructible using English words (even including transliterated place names). However, 11-squares are possible if words from a number of languages are allowed (Word Ways, August 2004 and May 2005).
Other languages[edit]
Word squares of various sizes have been constructed in numerous languages other than English, including perfect squares formed exclusively from uncapitalized dictionary words. The only perfect 10-squares published in any language to date have been constructed in Latin, and perfect 11-squares have been created in Latin as well.[9] Perfect 9-squares have been constructed in French,[10] while perfect squares of at least order 8 have been constructed in Italian and Spanish.[11] Polyglot 10-squares have also been constructed, each using words from several European languages.[12]
Vocabulary[edit]
It is possible to estimate the size of the vocabulary needed to construct word squares. For example, a 5-square can typically be constructed from as little as a 250-word vocabulary. For each step upwards, one needs roughly four times as many words. For a 9-square, one needs over 60,000 9-letter words, which is practically all of those in single very large dictionaries.
For large squares, the need for a large pool of words prevents one from limiting this set to «desirable» words (i.e. words that are unhyphenated, in common use, without contrived inflections, and uncapitalized), so any resulting word squares are expected to include some exotic words. The opposite problem occurs with small squares: a computer search produces millions of examples, most of which use at least one obscure word. In such cases finding a word square with «desirable» (as described above) words is performed by eliminating the more exotic words or by using a smaller dictionary with only common words. Smaller word squares, used for amusement, are expected to have simple solutions, especially if set as a task for children; but vocabulary in most eight-squares tests the knowledge of an educated adult.
Variant forms[edit]
Double word squares[edit]
Word squares that form different words across and down are known as «double word squares». Examples are:
| T O O U R N B E E |
L A C K I R O N M E R E B A K E |
S C E N T C A N O E A R S O N R O U S E F L E E T |
A D M I T S D E A D E N S E R E N E O P I A T E R E N T E R B R E E D S |
The rows and columns of any double word square can be transposed to form another valid square. For example, the order 4 square above may also be written as:
L I M B
A R E A
C O R K
K N E E
Double word squares are somewhat more difficult to find than ordinary word squares, with the largest known fully legitimate English examples (dictionary words only) being of order 8. Puzzlers.org gives an order 8 example dating from 1953, but this contains six place names. Jeff Grant’s example in the February 1992 Word Ways is an improvement, having just two proper nouns («Aloisias», a plural of the personal name Aloisia, a feminine form of Aloysius, and «Thamnata», a Biblical place-name):
| T R A T T L E D |
| H E M E R I N E |
| A P O T O M E S |
| M E T A P O R E |
| N A I L I N G S |
| A L O I S I A S |
| T E N T M A T E |
| A S S E S S E D |
Diagonal word squares[edit]
Diagonal word squares are word squares in which the main diagonals are also words. There are four diagonals: top-left to bottom-right, bottom-right to top-left, top-right to bottom-left, and bottom-left to top-right. In a Single Diagonal Square (same words reading across and down), these last two will need to be identical and palindromic because of symmetry. The 8-square is the largest found with all diagonals: 9-squares exist with some diagonals.
These are examples of diagonal double squares of order 4:
| B A R N A R E A L I A R L A D Y |
S L A M T I L E E A T S P R O S |
T A N S A R E A L I O N L A N D |
Word rectangles[edit]
Word rectangles are based on the same idea as double word squares, but the horizontal and vertical words are of a different length. Here are 4×8 and 5×7 examples:
| F R A C T U R E O U T L I N E D B L O O M I N G S E P T E T T E |
G L A S S E S R E L A P S E I M I T A T E S M E A R E D T A N N E R Y |
Again, the rows and columns can be transposed to form another valid rectangle. For example, a 4×8 rectangle can also be written as an 8×4 rectangle.
Higher dimensions[edit]
Word squares can be extended to the third and higher dimensions, such as the word cube and word tesseract below.[13]
K │I │N │G I │ D │ E │ A N │ E │ T │ S G│ A│ S│ H ────┼────┼────┼──── I │D │E │A D │ E │ A │ L E │ A │ R │ L A│ L│ L│ Y ────┼────┼────┼──── N │E │T │S E │ A │ R │ L T │ R │ I │ O S│ L│ O│ P ────┼────┼────┼──── G │A │S │H A │ L │ L │ Y S │ L │ O │ P H│ Y│ P│ E
ALA ROB TWO AEN TEU ARN RAA ARM EYE EAN IBA EAR SRI YAS RIE EAS OYE SAW SON AEA TST HAE ETH OII AMP REU SLE
Other forms[edit]
Numerous other shapes have been employed for word-packing under essentially similar rules. The National Puzzlers’ League maintains a full list of forms which have been attempted.
See also[edit]
- National Puzzlers’ League
- Sator Square
References[edit]
- ^ Ferguson, Everett (1999). Encyclopedia of Early Christianity (2nd ed.). Routledge. p. 1002. ISBN 978-0815333197. Retrieved 16 September 2022.
Rotas Sator (first century): Although the result is striking, the interpretation rests on the unlikely assumptions, and a non-Christian meaning is more probable.
- ^ «Sator square». Encyclopedia Britannica. Retrieved 17 September 2022.
- ^ Sheldon, Rose Mary (2003). «The Sator Rebus: An unsolved cryptogram?». Cryptologia. 27 (3): 233–287. doi:10.1080/0161-110391891919. S2CID 218542154. Retrieved 10 September 2022.
- ^ Griffiths, J. Gwyn (March 1971). «‘Arepo’ in the Magic ‘Sator’ Square». The Classical Review. New Series. 21 (1): 6–8. doi:10.1017/S0009840X00262999.
- ^ a b c d Eckler, A. Ross (2005). «A History of the Ten-Square». In Cipra, Barry Arthur; Demaine, Erik D.; Demaine, Martin L.; Rodgers, Tom (eds.). Tribute To A Mathemagician. A K Peters, Ltd. pp. 85–91. ISBN 978-1-56881-204-5. Retrieved 2008-08-25.
- ^ «Achalasia». Word Ways. August 2003.
- ^ Brandreth, Gyles (1986). Everyman’s Word Games. Book Club Associates. p. 90.
- ^ «Hunting the Ten-Square». Word Ways. May 2004.
- ^ Tentarelli, Eric (November 2020). «Large Word Squares in Latin». Word Ways. 53 (4).
- ^ Bartholdi, Laurent (1996). «Mots croisés mélanophobes» (PDF). Gazette des Mathématiciens (in French). 70.
- ^ Borgmann, Dmitri (1965). Language on Vacation. Charles Scribner’s Sons. p. 198.
- ^ Gooch, Rex (May 2004). «Hunting the Ten-Square». Word Ways. 37 (2).
- ^ Darryl Francis, ‘From Square to Hyperhypercube’, Word Ways: Vol. 4: Issue 3, Article 8, 1971
External links[edit]
- Word Square — Free to play double word squares
- Word Hash — Free to play word squares
- Stairsteps — Daily double word squares and rectangles — Free M-Th
I wanted to share a very simple, yet effective tool for helping students build vocabulary skills. Vocabulary Squares are a way for students to record new vocabulary terms, explore their meaning, and begin using them in communication.
When a student is introduced to a new vocabulary word or phrase, they can record information about it in a page like the one below (feel free to click on the link below the picture to open up a downloadable version).
Here’s how they work…
I generally have students record the following information in their vocabulary square:
- A good definition: This may or may not be the “dictionary definition.” See my post on Keeping it Simple to see some helpful tips on giving good definitions to your students.
- A “Sense” Sentence and a “Nonsense” Sentence: Either give the word in a sentence for context, or have students come up with their own sentences (make sure to check what they have written for accuracy!). The “Nonsense” Sentence can be a bit tricky, and I usually only do it with upper-level students (lower-leveled students would just have a “sense” sentence). Here, students should write down a sentence where the word is used with an incorrect meaning. For example, with the word impossible, students might have a nonsense sentence like: “It is impossible for me to come to school because my car is working fine.” Students can create their own sentences, or take an example given by the teacher. These nonsense sentences help students understand a broader range of the word.
- Synonyms and Antonyms: Students can use themselves, a thesaurus, or other resources to look up related and opposite words to give them a more concrete idea of the vocabulary term’s meaning.
- A picture: As the old saying goes, “a picture is worth a thousand words.” In this case, pictures are excellent for helping students to understand new words and be able to review them quickly. I usually have students draw a picture that helps represent the word; for example, for the word humongous, I might have a picture of an elephant next to a mouse, with an arrow pointing to the elephant.
Additional Ideas…
One of the best things about Vocabulary Squares is that you can quickly adapt them as needed. As I said before, “nonsense” sentences are difficult for low-leveled learners, so they can either be dropped or switched out for negative sentences. Students can either record their information as guided notes, or fill in their charts with their own answers–or even work in small groups. Also, instead of just synonyms or antonyms, students can also work on related parts of speech (i.e. quick (adj.) and quickly (adv.)). Lastly, it can be very useful for students to keep track of their vocabulary worksheets in a notebook or binder. That way, they can be reviewed at intervals throughout the class.
It really only takes a short time to edit the vocabulary square worksheet. What ideas can you think of for using it in your classroom?
SKIP TO CONTENT
-
word square a puzzle where you fill a square grid with words reading the same down as across
-
word stress the distribution of stresses within a polysyllabic word
-
discourse an extended communication dealing with some particular topic
-
herd’s grass grass with long cylindrical spikes grown in northern United States and Europe for hay
-
foursquare (geometry) a plane rectangle with four equal sides and four right angles; a four-sided regular polygon
-
least squares a method of fitting a curve to data points so as to minimize the sum of the squares of the distances of the points from the curve
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Pholiota squarrosa a gilled fungus with a cap and stalk that are conspicuously scaly with upright scales; gills develop a greenish tinge with age
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Rhodes grass perennial grass of South Africa introduced into United States; cultivated as forage grass in dry regions
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bird-scarer a human-shaped object used to keep birds away from crops
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wood sugar a sugar extracted from wood or straw
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word sense the accepted meaning of a word
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Wordsworth a romantic English poet whose work was inspired by the Lake District where he spent most of his life (1770-1850)
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grotesqueness ludicrous or incongruous unnaturalness or distortion
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grotesque distorted and unnatural in shape or size
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Earth’s crust the outer layer of the Earth
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fair-and-square just and honest
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grotesquerie ludicrous or incongruous unnaturalness or distortion
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red scare a period of general fear of communists
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transgress act in disregard of laws, rules, contracts, or promises
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grotesquery ludicrous or incongruous unnaturalness or distortion
Printables
As part of their vocabulary study, readers select unfamiliar words from their current reading assignment, record the etymology and part of speech, variations, the definition, and draw a symbol, logo, or icon. They then create a sentence that employs the word and reflects events in the story.
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CCSS:
Adaptable
Additional Tags
english language arts
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Instructional Ideas
- Separate the squares, write the word on the reverse side, and use the squares as flash cards for vocabulary review
Common Core
L.9-10.4.a
L.11-12.4.a
“Vocabulary Squares.” 15 Vocabulary Strategies in 15 Minutes. Learning Tasks. Web. 25 Apr. 2016 http://learningtasks.weebly.com/vocabulary-strategies.html
Vocabulary Square for the word “Voice” (Unfortunately, I could not implement my exact Vocabulary Square. However, I have attached a format of one and answered the specific sections.)
Part of Speech: noun
Synonyms: tone, message, attitude
Symbol/Logo/Icon: megafone
Definition: The form or a format through which narrators tell their stories. It is prominent when a writer places himself / herself into words and provides a sense the character is real person conveying a specific message the writer intends to convey.
Sentence: The author’s voice was very clear because of her word choice and imagery.
Relevance: This activity would be relevant to my unit as we will be reading multiple narratives in which author’s deliver messages using very distinct voices. In order to analyze this aspect of literature, students will need to understand what voice is in literature and writing. By creating the Vocabulary Squares, students will have the opportunity to make the connections to the word in several manners that can help them grasp the concept.