I have taught introductory physics with clickers many times, and do on occasion present clicker question sequences that "step through" what would formerly have been a traditional problem-solving example/demonstration on the board.

As a concrete example, there is a fairly canonical problem (solved in all texts in some form!), involving finding the electric field from a solid sphere of charge. It is a rather complicated problem, involving multiple steps that build on one another. For our purposes here, never mind the details -  what we did (and I stole this from Mike Dubson!) was to craft a sequence of clicker questions which involved what I considered the key steps in that derivation.  I asked the students to derive a formula for each sub-piece of the problem.  I "animated" the question slide so they first were asked to just do a little (one-step) derivation on their own, and only later (after giving them a few minutes to work on it) did I provide answers to click on (in the form of formulas, although one of was "something else")  This timing was an attempt to avoid them overtly "gaming" the system (I feared some students wouldn't work on it analytically, but just look at the multiple-choice answers and discard implausible answers) I was able to watch students - those who were not writing or gesturing or working were pretty apparent, so it was fairly easy even with 200+ students to get them all working on it.  The final clicker question in the sequence asked for a more general conclusion based on the work we had done, and was nice to consolidate the story and see if they were missing the forest for the trees. 

This worked out well - the derivation took considerably longer to get through, but the students had all worked on some of the steps. Even those who didn't get it correct had spent time thinking about what procedure they would need to use, and were thus primed for my explanations. What they did NOT get to do (which you might be after) was to decide at a higher level how to break up the problem in the first place, or which sub-part to tackle next, or why. This I facilitated through rhetorical questions, not clicker questions. So they were engaged in parts of the problem-solving story, but were "presented" with others. 

-Steven Pollock (CU Physics)