Wikipedia:Reference desk/Archives/Mathematics/2006 November 2

= November 2 =

Crossword grid search
I want to be able to find a crossword grid with certain specified constraints, e.g. to be square, have 180 degree symmetry, with all words the same length and for the number of across words to exceed the number of down words by 1. Rather than design a grid, it may be easier to select one from a standard bank. Does anyone know of such a source?

I emphasize that I'm not interested in filling the grid with actual words, i.e. it's not a crossword compiler program I'm after. My interest is in the structural properties of the grid when just the shaded squares are there.--86.132.166.128 18:20, 2 November 2006 (UTC)


 * If a grid is symmetrical and the word have the same length, how can across exceed downs ? -- DLL .. T 22:32, 2 November 2006 (UTC)


 * Easily - consider a 5 X 5 grid with the 2nd and 4th rows completely blocked in. All words have 5 letters, 3 across, none down. It depends on the type of symmetry. An example with only 180 deg symmetry - rows A to E, columns 1 to 5, block squares A 3-5, B 1-3, C 3, D 3-5, E 1-3 to give 10 2-letter words, 6 across and 4 down.


 * Is there a searchable bank of grids somewhere, or a program to generate them with the sort of requirement of which my initial example was typical?--86.132.166.128 00:09, 3 November 2006 (UTC)


 * While I don't know a definitive answer, I must say that both appear unlikely to me, and especially the existence of a grid bank that is searchable with this kind of constraint. Creating a generating program is probably feasible, although it may be hard to make it efficient. --Lambiam Talk  06:50, 3 November 2006 (UTC)


 * A trivial solution would be for one horizontal word through the middle of the grid and no vertical words. Any grid with an odd number of across words must have one through the middle, and the other words placed in pairs in a symmetrical fashion around it. Any grid with an even number of will have one symmetrically placed vertical word. Your faily free in the placement of other words, place one word and then rotate it through 180 degrees to find its pair. A corollary of this is that it only works for grids with an odd number of squares and words with an odd number of letters. --Salix alba (talk) 01:50, 5 November 2006 (UTC)