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Mahjong Connect
Connect is the flat cousin of the solitaire: the tiles lie in a single layer, nothing is covered, and a pair can be taken when a line of at most three straight segments joins the two tiles without crossing any other tile. The line may leave the board and come back along its edge. In Japan the game is called Shisen-Sho and it is older than most people think, from the early 1990s.
The two-turn rule is what makes it a puzzle. Neighbours are easy. Two tiles at opposite corners of an empty rectangle are easy. The pair that sits with one tile between them on the same row is not: the line has to go around, and around means a full detour with two corners, which needs a clear column on both sides. On a fresh board very few pairs are joinable, so the first moves come from the edges, and the board opens from the outside in.
Every deal starts as a full board of blank tiles. The program takes off pairs that can be joined at that moment, one after another until the board is empty, and writes matching faces into the places each pair left. That sequence is a solution, so there is always a way through. There is no gravity here: tiles stay where they are when their neighbours leave, which is the older and, I think, cleaner variant.
Three sizes: 10×6 for a phone, 12×8 for a desk, and 16×9, which uses the full set of 144 tiles. When two tiles you click do not join, the second one shakes, and when they do, the line is drawn for a moment so you can see the route it took.


