In a Bongard problem, you have to figure out what the rule is. You are given twelve specific images, and the result of applying the rule to each. (The rule assigns an image to either the left or right group.) Once you have discovered the rule, applying it to new images would be trivial.
The real world application of this, would only lead to dangerous assumptions. There is no practical application for this, it is like something Dinner for Schmucks invitees would engage in.
And many more such problems:
http://www.foundalis.com/res/bps/bpidx.htm