Word square

A word square is a special 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:

A popular puzzle dating well into ancient times, the word square is sometimes compared to the magic square, though apart from the fact that both use square grids there is no real connection between the two.

The Sator Square is a famous word square in Latin. Its canonical form reads as follows:

In addition to satisfying the basic properties of word squares, the Sator Square spread widely due to several other attributes: it is palindromic; it can be read as a sentence of obscure meaning; and additional meaning such as reference to the Christian Paternoster prayer can be derived from its letters. However, the word "Arepo" appears nowhere else in Latin literature; most of those who have studied the Sator Square agree that it is to be taken as a proper name, either an adaptation of a non-Latin word or, more likely, a name invented specifically for this sentence. Thus the square consists of a palindrome ("tenet"), a reversal ("sator" and "rotas"), and a word ("opera") which can be reversed into a passably coined name ("Arepo").

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".

No source or explanation is given for any of the "words", so this square does not meet the modern 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.

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