[Math] Deciding if a Solitaire game is solvable

card-gamescombinatorics

Is there a fairly straightforward procedure for determining if a given game of Solitaire (say Klondike) is solvable?

One of my students would like to write a Solitaire game and give an "always winnable" option. It is possible to take a won game and make random plays backwards to create a solvable game.

But my question is: Is there a test for seeing if a game is solvable that can be readily resolved by examining the state of the game?

Best Answer

Perhaps we can start pruning the search space by identifying characteristics of unwinnable games and searching for those.