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In Word Ways in August and November 2002, he published several squares found in this wordlist. 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 , though apart from the fact that both use square grids there is no real connection between the two. A two-letter combination in bold means that the link links straight to a Wikipedia article not a disambiguation page. Each such square contains five words appearing twice, which in effect constitutes four identical 5-squares.
It is possible to estimate the degree of difficulty of constructing word squares. IY wYeYnYtY tYoY tYhYeY bYaYtYhYrYoYoYmY aYnYdY gYoYtY hYeYrY hYaYiYrYbYrYuYsYhY IY gYoYtY iYnY tYhYeY rYoYoYmY aYnYdY tYoYlYdY hYeYrY tYoY bYeYnYdY oYvYeYrY tYhYeY bYeYdY. Each such square contains five words appearing twice, which in effect constitutes four identical 5-squares. 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.
- Its canonical form reads as follows.
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. 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 , though apart from the fact that both use square grids there is no real connection between the two. 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, the Sator Square spread widely due to several other attributes: it is ; it can be read as a sentence of obscure meaning; and additional meaning such as reference to the Christian prayer can be derived from its letters. An English edition appeared in 1898. 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. 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. It has been called the of. Each such square contains five words appearing twice, which in effect constitutes four identical 5-squares. The largest source was the. 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. 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. It is possible to estimate the degree of difficulty of constructing word squares. Roughly, for each step upwards, one needs four times the number of words. For a 9-square, one needs over 60,000 9-letter words, which is practically all of those in single very large dictionaries. The opposite problem occurs with small squares: a computer search will produce millions of examples, most of which use at least one obscure word. 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. 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. 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. This is an example of a diagonal double square of order 4: B A R N A R E A L I A R L A D Y 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. For example, a 4×8 rectangle can also be written as an 8×4 rectangle. Other forms Numerous other shapes have been employed for word-packing under essentially similar rules. The maintains a full list of forms which have been attempted.
Project Based Learning: Explained.
The opposite problem occurs with small squares: a computer search will produce millions of examples, most of which use at least one obscure word. KYiYmY'sY PYOYVY IY hYoYpYeYdY iYnY tYhYeY sYhYoYwYeYrY aYnYdY nYoYtYiYcYeYdY tYhYaYtY IY tYoYoYkY tYoY lYoYnYgY sYoY IY rYiYnYsYeYdY mYyY hYaYiYrY aYnYdY hYoYpYpYeYdY iYnYtYoY mYyY sYkYiYnYnYyY jYeYaYnYsY aYnYdY tYaYnYkY tYoYpY tYhYeYnY pYuYtY oYnY mYyY bYlYaYcYkY vYaYnYsY. Once the disambiguation page has been created, the other variant should to that page. IY sYtYaYyYeYdY iYnY bYeYdY cYaYuYsYeY IY dYiYdYnY'tY wYaYnYtY tYoY gYoY tYoY sYcYhYoYoYlY tYoYdYaYyY. This is an example of a diagonal double square of order 4: B A R N A R E A L I A R L A D Y 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. SYoY wYhYeYnY yYoYuY aYrYeY dYoYnYeY eYaYtYiYnYgY gYoY tYoY mYyY rYoYoYmY aYnYdY IY bYeYtYtYeYrY sYeYeY yYoYuY iYnY tYhYeY cYoYrYnYeYrY bYaYrYeY.
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