For anyone not familiar with the math of Set, let me shamelessly plug "The card game SET", by Ben Davis and Diane Maclagan, in Math. Intelligencer 25 #3 (Summer 2003), for which I was (a very hands-on) editor. You can find a pdf of it on my publications page, http://people.brandeis.edu/~kleber/pubs.html . Dan asks:
The online game is here:
< http://www.nytimes.com/ref/crosswords/setpuzzle.html >,
QUESTION: What makes one 3x4 array with 6 sets among them "harder" than another? (I often find this online puzzle's "level 4" to be easier than its "level 3", so this has me wondering.)
All sets (ie lines in (F_3)^4) are affinely isomorphic, certainly, but from the card game point of view, they can be easier or harder to spot, depending on which attributes vary and which are fixed. In my experience playing the game, the hardest sets to spot seem to be those in which three of the four attributes vary and one stays fixed, though I don't know why this should be true (and maybe it isn't really; I only have a subjective feeling, not any actual data). That said, the number of fixed attributes in the six sets from today's level 3 and 4 puzzles were (3,2,2,1,1,0) vs (3,3,2,2,1,0) respectively, so I'd have guessed level 3 to be the harder one on these grounds. So much for that hypothesis. Which attributes they are probably matters too -- I know I feel more stupid about being slow to see a set when it turns out to be monochromatic, for example :-). --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.