A word square is a kind of acrostic. It is formed of several different words, all of the same length. The words contain as many letters as there are words across or down (known as the "order" of the square). When the words are written one under each other, the same words read both horizontally and vertically. A popular puzzle dating well into ancient times, the word square is related to the magic square. An acrostic (from the late Greek akróstichon, from ákros, extreme, and stíchos, verse) is a poem or other text written in an alphabetic script, in which the first letter, syllable or word of each verse, paragraph or other recurring feature in the text spells out another message. ... In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. ...

Examples

Here are examples of English word squares up to order eight:

The acceptability of a word square depends upon its size: for a 4-square it is reasonable to require all words to be recognisable by a child. As the size increases, the number of possible squares eventually decreases extremely rapidly. Hyphens, apostrophes, capital letters, and words last in use hundreds of years ago are to be avoided if possible. Some even mandate all words are to come from a named dictionary. However, such restrictions sometimes produce unwelcome results: for example, most people would prefer a well-known place name like Manchester to an obscure Anglo-Saxon word. The larger the square, the more such restrictions bite. The 8-square above contains words not familiar to most educated adults. Regarding 9-squares, it is just possible (but only in 2003) to find a 9-square whose words are all contained in the combined OED, Webster 2, and Chambers.

This "perfect" order 9 square (all words in major dictionaries, no hyphens, no capitals, no apostrophes) is in Word Ways August 2003, along with others similar:

A 10-square is naturally much harder to find, and has been hunted for 80 years: it has been called the Holy Grail of logology, and its finder has been promised immortality. It cannot be constructed from dictionary words alone, but can be if we permit words in gazeteers. This kind of escalation of word sources with increasing difficulty is a widely accepted necessity in logology, especially when, as in this case, there is strong proof (both mathematical and experimental) that no combination of dictionaries would suffice. Jeff Grant had a long history of producing ever better 10-squares, then Rex Gooch produced a great leap forward (Word Ways, August 2002). In the November 2002 Word Ways, he published some better squares, and the one below is regarded by all the word square experts as the best, and as essentially solving the problem (this statement has been verified by the Daily Mail and The Times newspapers by correspondence with the appropriate people). An account of how the ten-square was found is in 'Hunting the Ten-Square' in Words Ways May 2004 (available on the Internet). The last few years have seen a large number of new large word squares, and even new species. But above all, word squares have been put on a scientific basis: we can, for example, say that 250000 10-letter words are needed to make a 10-square: compare this to perhaps 50,000 in the world's largst dictionary. That explains why it took so long to find, and points the way ahead.

There are few imperfections: Echeneidae has a cap, Dioumabana and Adaletabat are places, and nature-name is hyphenated. The square is certainly the pinnacle of hard core logology.

Eleven-squares are far harder again to construct, and cannot be done using English words (even including transliterated place names). However, it is possible by using words from a number of languages (see Word Ways August 2004 and May 2005).

A 12x12 word square appears in the book The Book of the Sacred Magic of Abramelin the Mage: ^{[clarification needed]} Cover of a 1975 paperback reprint of Mathers 1897 English translation of The Book of the Sacred Magic of Abramelin the Mage ; the art is an etching by Rembrandt titled Dr. Faustus and has nothing to do with the story of Abramelin. ...

No sourcing is given for any of the words: a 12-square is most likely impossible with normally available words or names, whatever the languages.

Sator Arepo Tenet Opera Rotas is a famous palindromic word square in Latin which also forms a sentence, though its meaning is dubious. The words of the sator square may be read in any direction SATOR AREPO TENET OPERA ROTAS (sometimes called the sator square) is a Latin palindrome, the words of which, when written in a square, may be read top-to-bottom, bottom-to-top, left-to-right, and right-to... A palindrome is a word, phrase, number or other sequence of units (such as a strand of DNA) that has the property of reading the same in either direction (the adjustment of punctuation and spaces between words is generally permitted). ... Latin is an ancient Indo-European language originally spoken in Latium, the region immediately surrounding Rome. ...

Diagonal word squares

are word squares in which the main diagonals are also words. There are three diagonals: running to the NW, running to the SE, and a palindromic one. The 8-square is the largest found with all diagonals: 9-squares exist with some diagonals.

Double word squares

Word squares that form different words across and down are known as "double word squares". Examples are:

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:

This is a double word square whose corner-to-corner diagonals are also words:

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.

Word rectangles

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:

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.

See also

• Sator Arepo Tenet Opera Rotas