It's easier than you think -- the problem is to find a characteristic or rule that all of the lefthand objects conform to, and that all of the righthand objects do not.

The problem is not (as is sometimes the case for similar-looking IQ test problems) to find a rule that transforms the left side of each pair into the right side, or that generates the whole sequence of six iteratively. That might have been what you were searching for; I tried to do so in vain before reassessing the problem!

Technically, the "first" Bongard problem is much simpler: http://www.foundalis.com/res/bps/bongard/p001.htm

Since this was hard to find, here's the full index: http://www.foundalis.com/res/bps/bpidx.htm

Haha, I felt smart for a second because I got the "non-trivial" example immediately, but then realized my browser history for the past month consists of research on convex vs non-convex optimization problems, so I feel I had a bit of an unfair advantage there.