Everyone who plays mahjong solitaire knows the moment: no moves left, twenty tiles still on the board and none of them matching. You did not make a mistake. The board could not be solved in the first place.
Where the problem comes from
The classic method is this: scatter 144 tiles onto a skeleton at random, let the player play.
With that method, whether the board is solvable is left to chance. Worse, the player can make it unsolvable while playing: two tiles taken in the wrong order can lock a pair underneath forever.
Some games paper over this with a shuffle button. But a shuffle is not a solution, it is a confession.
Balbal's method: solution first, board second
The order is reversed.
- First the skeleton — the silhouette of the board — is fixed.
- Then a valid removal order that clears that skeleton is generated.
- The tiles are placed by matching consecutive pairs from that order.
Step three is the heart of it. The first and second tiles in the removal order take the same symbol, the third and fourth take the same symbol, and so on. The board that comes out already has its solution in hand: follow that order and the board clears.
The tray makes it harder
In Balbal a match is not immediate; the tile you take goes into a tray of four slots and waits there for its twin. So for a solution to be valid it must also not overflow the tray.
Generation accounts for that. The guarantee:
An order that clears the board using at most two tray slots always exists.
The player has four. Two slots more than the guarantee — room to be wrong.
The proof reruns on every release
This is a test, not a design promise. All 1500 levels are played end to end by a simulated player on every release. If there is a board it cannot solve, the release does not ship.
The same test measures the difficulty curve: how many moves a level takes, how often three tray slots fill up, how far each level strays from the average.
And if you still lock up?
Locking up is still possible — a solution existing does not mean you will find it. That is what the three helpers are for: Shuffle redeals the board, Hint shows a matching pair, Undo puts the last tile back.
The difference is that in Balbal a shuffle is a convenience, not a confession. The board was solvable without it.
See also: How the game works · How to play