When you are at the unsolvable situation, take a look at which tiles you currently have left that are free and open. If you want a more challenging way of getting out of this situation, you need to undo back to the point where things got out of hand.
If you end up in an unsolvable situation, the easiest solution is to shuffle all the remaining tiles, generating new pairs of tiles and allowing you to continue playing. You end up in an unsolvable situation when you have matched the wrong pair of identical tiles earlier on. See what tiles you need to match first, in order to pair up hard-to-match tiles later on. There is always at least 1 solution, but certain boards are tougher than others, requiring you to match specific tiles in a specific order.
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Here are some good tips and solving techniques on how to play Mahjong Solitaire puzzles: This means that there is at least one valid solution to the board: the way it was generated.
A Mahjong Solitaire board puzzle in computer games are generated by actually playing the game in "reverse", placing two and two identical tiles on top of each other, while when solving it you play it the other way around. Solving a Mahjong Solitaire board puzzle is all about avoiding getting to the situation where there are no available matches left (but still tiles left on the board).
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