Daily Mahjong Solitaire

Mahjong Solitaire takes the 144 tiles of the four-player game and stacks them into a single shape, here the classic Turtle: five layers, highest in the middle, with a lone tile on the summit. You clear it two at a time. Pick any two matching tiles that are free, meaning nothing sits on top of them and they can slide out to the left or the right, and they leave the table. Empty the table and you have won.

There is one layout a day, the same for everyone, and it changes at midnight UTC. Before a layout goes live our solver clears it completely, and that clearance is replayed through the game itself, so today's tiles can always be cleared. If you get stuck, Hint points to a pair, Shuffle rearranges what is left into a position that can still be won, Undo goes back as far as you like, and the calendar holds every past day.

Mahjong Solitaire rules

• The Turtle holds 144 tiles in five layers. Most of them are in the wide bottom layer, and each layer above is smaller, up to the single tile on top.
• A tile is free when no tile lies on it, even partly, and its left or right side is open. Tiles above and below in the same layer don't block it; only the neighbours to the left and right do.
• Click two free tiles with the same face to remove them. Clicking a blocked tile greys out every tile that is not free, so you can see at a glance what is playable.
• The suits are dots, bamboo and characters, each numbered 1 to 9. Then come the four winds and the three dragons. There are four copies of each of these tiles, and a tile only matches an identical one.
• The eight bonus tiles are the exception. There are four flowers and four seasons, all with different pictures, but any flower matches any flower and any season matches any season.
• You win when the table is empty. If no free tiles match, the game is stuck: Undo a few moves or press Shuffle.
• The clock starts at your first click. Each Hint and each Shuffle adds 20 seconds to your time; Undo, Redo and Restart are free. New game deals another layout at the level you choose: Easy, Medium or Hard.

Why some Mahjong deals cannot be won

Deal 144 tiles into the Turtle at random and some layouts are dead before the first click. The simplest case is three copies of one tile stacked straight on top of each other. The top one can pair with the fourth copy elsewhere, but then the middle one needs a partner, and the only one left is underneath it. No order of moves untangles that. A large published analysis of ten million random Turtle deals found about 3 in every 100 have no solution at all, even for a player who can see every tile.

Many more deals are winnable but easy to lose. Every pair you take changes which tiles open up next, and with four copies of each face there is often a choice of which two to pair. Pick wrongly early on and the game can lock up dozens of moves later. That is why we never hand out an unchecked deal: the daily layout, and every layout behind New game, has been cleared by our solver from start to finish and the win replayed in the game.

How hard is a Mahjong layout?

Our solver dealt 15,000 random layouts and played each one twenty times the way the tips below suggest: it looks at what every pair frees, works the high stacks first and never leaves a tile lying on its own twin. Only the 6,037 layouts it cleared at least twice, with the win replayed through the game, are used here. Even on those it wins only about 30% of its games, so a layout that can be won is not the same as an easy one.

The daily layout is always one of the friendliest: the solver clears it in at least two games out of five, so careful play has a real chance of clearing it without help. In New game, Easy, Medium and Hard split the rest by how often the solver wins them. On Hard layouts it loses most of its games, and the choice of which pair to take matters from the first few moves.

The Mahjong tiles

The set has 34 different faces, four copies of each. Three suits run from 1 to 9: dots, bamboo and characters. Then come the four winds, east, south, west and north, and the three dragons: red, green and white, the white one drawn as a blue frame.

The last eight tiles are four flowers and four seasons, each with its own picture. They are the only ones that do not need an exact twin: any flower pairs with any flower, and any season with any season. If some faces look alike to you, turn on tile labels in Settings to put a small number or letter on each tile.

Buttons, keys and settings

Hint shows a pair you can take, picked where possible from a full solution of the position you are in. Shuffle rearranges the tiles that are left into a position that can still be cleared, and a small number on the button counts your shuffles. Each of them adds 20 seconds. Undo and Redo step back and forward through your moves as far as you like, and Restart starts the same layout again. The game is saved in this browser as you play, so you can close the page and carry on later.

On a computer you can play from the keyboard: Q or H for a hint, S to shuffle, Ctrl+Z to undo and Ctrl+Y to redo. Tab to the board and the arrow keys move between the free tiles, with Enter to pick one. In Settings you can turn on tile labels, which put a small number or letter on each tile and show its name beside the mouse, light up free tiles as the mouse passes over them, switch on sound or automatic hints, zoom the board, and choose the tile colour and the table.

Playing Mahjong Solitaire well

• Don't take a pair just because you can see it. Ask what each removal frees. A pair that opens two new tiles is worth more than one at the edge of the bottom layer that opens nothing.
• Open the long rows early. In the Turtle, a lone tile on the far left and two on the far right close off the ends of the widest rows. Until they go, those rows can only be worked from one side.
• Dig into the middle. The centre stack is five layers deep, and every tile under it stays locked until the tiles above are gone. The flat outer edges are easy to clear at any point, so leave some of them for later.
• When all four copies of a face are free, take both pairs straight away; it can't hurt. When three are free, stop and check which one is blocking something before you choose two of them.
• Watch for a tile lying on its own twin. The top one must be paired with one of the other two copies, so don't use those two on each other, or the bottom tile can never come out.
• Use Undo to test an idea before reaching for Shuffle. Undo costs nothing, while a Shuffle adds 20 seconds and replaces a position you may have nearly solved.