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Can This Game of Solitaire Be won

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Hi all, I have written a nice(ish) looking game of solitaire in Windows Forms, using VB.NET and Visual Studio 2015. It allows the player to play the game, and if their score is in the top 10, it saves the username and score o a leaderboard (saved in a text file so it is non-volatile). My next goal is to let the user know if the hand they are dealt is playable, but I'm not sure on the most efficient way of achieving this. I'm working on time complexity over space complexity! It's a simple game to code, but not an easy one to find the solution. Do you know of any algorithms that may achieve this goal that I would be able to look at?

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