Random Nation

You know, I was talking about randomly generated puzzles, and I didn't notice pretty much every computer with Windows has a couple of them in. Just open the tab 'Games' and check any of the solitaire games. Specially Freecell, which has no invisible component from the start: All the cards are open to see and consider the strategy.

What makes solitaire games capable of such randomizing? For one, there's a lot of leeway in what moves you can make (Freecell allows you to play any red card on any black card of a value one number higher, as well as four 'free cells' that can be used for storage of any card). The number of free cells could be changed to alter difficulty, even. Choose 500 games randomly, see how many can be solved with each number of free cells or card stacks.

So it appears that the easiest way to make random solvable puzzles is to either have a generator we know will make a solvable game, or have a variable that can be adjusted to make unsolvable games solvable. An automatic solver is also pretty helpful in that bit, so you can check for move count, alternate solutions and whatnot.

Now, what can I apply this stuff to.