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However, 11-squares are possible if words from a number of languages are allowed (Word Ways, August 2004 and May 2005).

Roughly, for each step upwards, one needs four times the number of words.

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. Each such square contains five words appearing twice, which in effect constitutes four identical 5-squares.

Since 1921, 10-squares have been constructed from reduplicated words and phrases like "Alala! 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: In 1976, Frank Rubin produced an incomplete ten-square containing two nonsense phrases at the top and eight dictionary words.

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): Diagonal word squares are word squares in which the main diagonals are also words.

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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.

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.