Ed Pegg Jr., May 10, 2004
For a long time, my top reference has been The Master Crossword Puzzle Dictionaryby Herbert M. Baus. Back when it was available, after hearing many glowing recommendations, I bought a remaindered copy for $8. Soon after that, the book went out of print, even though it remained the best book of its kind. It became a top seller on E-Bay, often fetching more than $800. Today, though, Baus (as it is called) has a rival. The Million Word Crossword Dictionary by Stanley Newman and Daniel Stark ($18) is just as comprehensive and useful. After using MWCD extensively, it's my new top reference.
The rules for American crosswords are as follows:
In addition, there is a tendancy for crosswords to have odd-valued sides, with 15×15 (not 14×16) being the predominate size for daily crosswords. One might wonder how many different crossword grids exist. It isn't too difficult to figure out the maximum possible number of words in a 15×15 puzzle (what is it?). The lower bounds are more obscure, since they are determined by vocabulary. Wide-open spaces are desirable in crosswords. The largest I know of are a 7×7 space, and a 4×15 space. For grids with a lively vocabulary, the puzzles below were all record-setters published in the New York Times.
|Frank Longo -- 54 words -- 24 Oct 97||Manny Nosowsky -- 21 Squares --7 Jan 00||Joe DiPietro -- 20 squares -- 19 Jan 01|
How are crosswords made? Until the era of personal computers, they were made by hand, and made very well. For example, given an area to fill in, the last letters of words are typically S, E, R, D, T, L, G, or N, so putting a word with a lot of those letters at the bottom will make things easier. The second letters of words are typically vowels, L, or R. Some words (AIRIE, ERNE, ...) became known as "crosswordese". Most constructors used word lists to aid them, along with a learned knack for how words fit together.
The original word puzzles were known as forms. The first order-6 word square was published in Godey's Lady's Book and Magazine in 1862 (below). Many other form types were developed by a variety of puzzling groups. The National Puzzler's League was one of them, founded on July 4, 1883. The NPL is still around -- you can read about the variety of forms at the NPL website, puzzlers.org.
Forms became increasingly popular. From June 1908 to March 1920, there was a magazine (The Former) devoted to them. In 1913, Arthur Wynne published a "word-cross" similar to the "hollow diamond" forms of the day in the New York World. In 1924, Simon and Schuster took a chance on publishing a book devoted to crosswords, and the crossword craze started. Crosswords have been published ever since. Forms continued to be made, as well, within the publications of the National Puzzler's League.
Crosswords tended to have easy words, familiar to everyone. Forms tended to have obscure words, requiring many expensive reference books. Familiarity ultimately won out over obscurity. Along with that, crosswords became much more popular than forms.
In 1989, Eric Albert used a wordlist of the 63,000 9-letter words in Webster's Second New International Dictionary, and had a computer program find all possible 9-squares. (Read more at puzzlers.org). After several weeks, he found a single example. Shortly afterward, he turned his program over to making crosswords instead. Part of his method involved carefully rating every word in his extensive wordlist, so that any puzzle his program created would be the best possible for that word list.
You can get a similar program with Crossword Compiler. A program can make thousands of puzzles for you, but they require a considerable amount of crafting to produce anything good. Look at Rule #9, above. The vocabulary must be lively and familiar to most people. My own first New York Times crossword made the grade because I used words like TEAKETTLE and KLEENEX in abundance. Big lists are available at Grady Ward's Moby lists, the Oxford wordlists, and the Brian Kelk lists. Carefully honed lists are not publicly available, so far as I know.
As a demonstration, I combined a number of mathematical sources to produce a mathematical word list. Parts of it are likely too obscure. Feel free to use any references you can think of to solve it. If you don't have Java, you can refer to the following Grid.
1. Cut corners
If there is enough interest, I may take the time to hone my list of mathematical words. Scoring a list creates lots of hard choices. For example, on a scale of 1 to 10, how should Edmund Landau be rated for familiarity among math enthusiasts?
Within the front matter, the authors of the Million Word Crossword Dictionary promise to consider all suggestions for new words and clues, for future editions. I'll suggest more math. If the book is successful, then its future as a top reference is assured, and the book will remain inexpensive and in print. That's what I'm hoping for. If it isn't successful, then the price of the existing copies may well match those of Baus's work, eventually.
The enumeration of fillable grids that meet the rules will likely stay unsolved for a long time.
References:barelybad.com, A Monograph on Crossword Puzzles, http://barelybad.com/crossword.htm.
Math Games archives.
Comments are welcome. Please send comments to Ed Pegg Jr. at firstname.lastname@example.org.
Ed Pegg Jr. is the webmaster for mathpuzzle.com. He works at Wolfram Research, Inc. as the administrator of the Mathematica Information Center.