The app would incorporate the "Freemium" model.
Like I said, there will be 30+ (about 35) different 'types' of problems to start with, some more complicated than others. There would be a free version available that has, say, 10-15 basic topics while the remaining topics would be considered "Premium" and their use would incur a one-time cost.
The cost would be relatively low (relative to the typical cost of software) and would be a one-time charge. We would plan on rapid releases with new features and bug fixes. The new, upgraded versions of the app would be offered to current users at discounted prices but the one-time payment would get you a lifetime of use for the version you purchase so upgrading would only be necessary if you were interested in the new features.
Additionally, critical fixes would be released to all users so no one would be hung out to dry if, for some reason, there was a problem with the core application.