Castle Mahjong

Castle is our own layout for Mahjong solitaire: a courtyard of 10 by 8 tiles, a wall of 8 by 6 tiles on top of it, and a tower of 2 by 2 tiles on each corner of the wall. You clear it by taking the 144 tiles off two at a time, each pair the same tile, and only tiles that are free. A tile is free when nothing lies on it and its left or right side is open. Flowers pair with any flower and seasons with any season.

The tiles, the controls and Shuffle work as on the turtle; the Mahjong Solitaire page explains each tile.

The ground floor is a solid courtyard of 80 tiles in eight rows of ten. On it stands the wall, 48 tiles in six rows of eight, set one tile in from every edge. The four towers, 2 by 2 tiles each and 16 in all, stand on the wall's corners.

So the courtyard's outer ring, 32 tiles, is never covered: those tiles are stuck only by their neighbours in the row. Everything inside the ring waits for the wall above it to go, and the wall's corners wait for the towers.

At the start 36 tiles are free: the ends of the eight courtyard rows, the ends of the wall rows that no tower covers, and the tops of the towers.

• Take the towers early. Each one covers four corner tiles of the wall, and the wall covers most of the courtyard.
• Work each long courtyard row from both ends: a row of ten opens one tile at a time, so a pair that frees a row end is worth more than a pair from the middle of the wall.
• Watch the four wall rows that run under the towers: their corner tiles stay blocked until the tower above is gone, so a tile you need may be trapped there.
• With 36 free tiles at the start you usually have 8 to 15 kinds to pick from. Use the first moves to open rows, not just to make pairs.

We built 1,049 Castle deals, each from a way to clear it. Our solver then had to find its own way through each one; it cleared 1,000 of them within its search limit, and those are the deals you play here. The 49 it could not finish in time are left out.

Across 300 of these deals, the first position offers on average 11.6 kinds of tile with a free pair (8 at the fewest, 15 at the most). The turtle offers 10.8, so the Castle opens a little wider.