The curiosity that the blanks in the solutions almost always are arranged in a backward diagonal is explained by the fact that English words have many common motifs, like “er”, that are more frequent than their reversals (“re” not so common). But I did manage to find a solution without this pattern of blanks: T E R C E N L O S I N G T A L E N T A A N G E L L A N D R O E N D E R S N G R A C I -Veit
On Jun 2, 2017, at 8:20 AM, Veit Elser <ve10@cornell.edu> wrote:
I’ve been playing with crossword puzzle variants. Here’s one that Dan A. will like.
1) The puzzle grid is an N by N torus. 2) In each row and column there should be exactly one black square.
For example, here is a solved 7 by 7 puzzle (black -> blank):
A D E R L E L E D S E A E R L E T T D W A N T E L A D D E R S E N D E R E A T E R H
To avoid trivial solutions we should require that the horizontal words are not all the same — as in this one. Still, the solutions I’m finding all have lots of symmetry. Note that the vertical words in this solution match the horizontal words.
Now here’s a challenge. Find a solution, with no repeated horizontal words, but where the black squares do not form a backward diagonal.
-Veit _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun