3d puzzle game generating levels

Question

I want to create a puzzle game for my first year in college. I will use OpeGL and C++.

The point of the game is to create a path between squares that have the same color, without making the paths intersect each other.

This is the game I want to reproduce: http://mypuzzle.org/3d-logic-2

When I first told my teacher that I want to create this game, I told him I will generate levels, not store them internally.

Then when I actually give it a little thought, I realised I don't have a great idea, just a bad-medium idea (one that doesn't generate "good levels", levels that are actually hard, that use as much space as possible, levels that have multiple solutions).

So my question is:

Does anyone of you know a great idea, an algorithm, some math etc. to use it to generate good levels?

Answer 1

Build a solver, and let it "grade" how good your random level is, and if it's good enough, present it to the user, otherwise generate another random level. That way you can place into the grading function what is required to be considered good.