|
||
|
Title: Xword Clues Post by Noke Lieu on Jan 21st, 2010, 6:30pm So, a crossword puzzle (following the usual rules of layout), that's n x n squares... what can you say about the number of clues? What if the cross word was (n x m) ? (sorry, a slow start to the year... :'( ) |
||
|
Title: Re: Xword Clues Post by Ronno on Jan 21st, 2010, 7:58pm The minimum number of clues is probably Floor[(n+1)/2]*Floor[(m+1)/2] The maximum depends on certain constraints, such as: 1. How short words are allowed? 2. Can the crossword be divided into separate sub-crosswords? |
||
|
Title: Re: Xword Clues Post by Noke Lieu on Jan 23rd, 2010, 7:28pm Nice, but I was thinking of something much more pedestrian... (and now filled with a sense of uncertainty thinking through 2x2 a bit more openly...) |
||
|
Title: Re: Xword Clues Post by Noke Lieu on Jan 24th, 2010, 10:55pm I was originally thinking that the crossword requires 4 fold rotational symmetry. |
||
|
Title: Re: Xword Clues Post by towr on Jan 25th, 2010, 1:43am I've seen enough crosswords that aren't in any way symmetric. |
||
|
Title: Re: Xword Clues Post by Grimbal on Jan 25th, 2010, 8:00am Around here (Geneva, french-speaking) they are never symmetric. It seems to me UK or US crosswords tend to be symmetric. I guess building crosswords is more difficult in some languages, making it too troublesome to make them symmetric. |
||
|
Title: Re: Xword Clues Post by rmsgrey on Jan 26th, 2010, 4:30am As long as both n and m are greater than 1, there are at least two clues. Assuming answers must be at least 3 letters, and that black squares separate answers, there's an upper bound of (m+1)n/4+m(n+1)/4 - if you add an extra column of black squares to the right of the grid, each across answer uses at least 4 squares - 3 letters and a black square - and similarly for down answers. |
||
|
Powered by YaBB 1 Gold - SP 1.4! Forum software copyright © 2000-2004 Yet another Bulletin Board |