Deciding if a Solitaire game is solvable

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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?

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