A tile is "free" when:
Two tiles are identical if they look exactly the same (of course...). An exception to this are the Flowers and Seasons tiles. They are non-identical matching tiles and belong to the same type. All the Flowers tiles match one another and all the Season tiles match one another. You should study them before starting a game.
Each tile appears four times in a standard solitaire mahjongg game. Again an exception for the Flowers and Seasons tiles who appear only once each during a game.
It's not as
easy as it sounds; you can end up with having matched the "wrong"
pairs and you may find yourself stuck, with
unmatchable tiles blocking other key tiles so you can't clear the layout. You
must be careful before removing a pair, you should look for where the remaining
pair is in the layout and plan ahead. If all four of an identical tile are free,
remove them to 'unclutter' the field. It's
not only a game of pure luck, you have to play strategic.
A Mah-Jongg set consists of 144 tiles. These are split in seven groups, called sets. The three first sets are numeric and they are called suits. The winds and the dragons tiles are called honor tiles. Remember: In the same way as playing cards can have different images for kings and queens, the look of the Mah Jongg tiles differs from game to game. This is specially true for flowers and seasons tiles. And in addition you can often make your own tile sets with pictures of your own choice. The images below are taken from the freeware game 'Dragonboard'.
The top row of each tile set contains the 9 ball tiles (also known as 'circle', 'badges' or the 'dots' tiles). Their numerical value (1 to 9) are represented by the number of balls shown on the tiles. There are four tiles of every Ball (36 tiles total).
The second row from the top contains the 9 bamboo tiles (also known as 'sticks' or 'bams'). Their numerical value (1 to 9) are represented by the number of sticks shown on the tiles. There are four tiles of every Bamboo (36 tiles total). A peacock, a rice bird or a real Mah Jongg bird  (a Sparrow) or occasionally a bamboo shoot which resembles a pineapple is shown on tile number one.
The third row contains the 9 characters tiles (also called the 'number', 'Wan', 'Ten Thousand' or the 'craks' tiles). The red symbol is the Chinese sign for 10.000 (and the sign for prosperity). The black symbol above are the sign for the numbers from 1 to 9. That would make them numbers from 10.000 to 90.000. Many games have put Arabic numbers on the corresponding tiles to help people from the western world. There are four tiles of every Character (36 tiles total).
The fourth row starts with the four seasons tiles. Contrary to the above mentioned suits the seasons tiles only appear once each in a game (4 tiles total). From left to right: Spring, Summer, Autumn and Winter. Printed above is the the corresponding abbreviations for the seasons. These tiles can either have an image or a Chinese symbol. When you play solitaire mahjongg games any season will match another season.
The fourth row end with the four wind tiles. From left to right: East, South, West and North. Shown on every tile is the Chinese symbol for the according wind. Again, in computer games, we cheat: The first letter of the wind is printed using Latin characters. There are four tiles of every wind (16 tiles total).
The fifth row starts with four flowers tiles. Just as the seasons tiles, the flowers tiles only appear once each in a game (4 tiles total). From left to right: The Orchid, The Plum Blossom, the Bamboo and the Chrysanthemum. Printed above is the the corresponding abbreviations for the flowers. When you play solitaire mahjongg games any flower will match another flower).
The fifth row ends with the dragons tiles. From left to right: Green Dragon, White Dragon and Red dragon. The white dragon can be a blank tile tile, or it can have an image of an rectangle (outlined in red or blue). There are four tiles of every dragon (12 tiles total).
(Taken from 'Shanghai Second Dynasty' Help):
'Mah jong' can be translated from Chinese as
'clattering sparrow', 'flax sparrow' or possibly as 'hemp bird'. The tiles when shuffled
make a melodious noise reminiscent of the noise of numerous sparrows squabbling
over scattered food crumbs.
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