Bongard Problems

[TheGreatErenan]

Well, I'm not, like, the boss or anything, but in my opinion, pretty much the only rule that really matters is that the correct solution should be plainly the correct intended solution more than any other potential solution.

For instance, with this one:

Group A:

banana
color
belvedere
hindsight
humbug
pascal

Group B:

tricycle
balrog
minus
random
wellington
kangaroo

There is the trivial solution that Group A contains words that are members of the set {banana, color, belvedere, hindsight, humbug, pascal}, whereas Group B contains words that are not members of that set. But obviously if you make up a puzzle with a solution like that, then you're kind of missing the point.

So I'd say, yes, you can have multiple parameters, but I would advise caution. Here are some notes from http://www.foundalis.com/res/invalBP.html:

• A note about "if ... then ..." rules: Strictly (and logically) speaking, these rules should be allowed. It turns out, however, that such rules can be very tricky and counter-intuitive for us, mere mortal, non logico-mathematically oriented humans. For example, consider the seemingly simple rule: "If there is a triangle then it is isosceles". So what if there is no triangle in one of the boxes at left? Apparently the box would satisfy the rule (since the premise is false), so it should be placed on the left side. We could then have a Bongard problem showing just one isosceles triangle in one of the six boxes on the left, with the other five boxes containing irrelevant (non-triangular) shapes, and all boxes on the right containing at least one non-isosceles triangle (among other shapes). Such a problem would be extremely hard to solve. Besides, it would be possible for one to postulate weird "if ... then ..." rules for most of the hard problems which contain a different, elegant solution, and thus render them trivial. So, I believe, "if ... then ..." rules should be avoided, not because they are logically impossible, but because they do not comply to the spirit of BPs, which is to probe common-sense intelligence.
• For reasons similar to the ones explained above, rules consisting of long sequences of disjunctions ("... or ... or ...", etc.) should be avoided. Again, one can turn the most elegant problems to trivial ones in this way. Two clauses, however, ("... or ...") do not seem to be an extreme thing to consider.