1. Simplicity.
A "complex" puzzle game is not appealing to many people. Tetris was simple, Columns was even simpler. You fit the blocks, once it makes a row, they disappear.
2. Difficulty Ramping.
Puzzle games need to start off slow, teaching you the concepts without too much chance of you messing up. By the time it gets to harder levels, you should know enough to at least BELIEVE you can cope with the difficulty.
3. Surprise.
In all its simplicity, some of the best puzzle games introduce the element of surprise ( or variety ). Witness the "magic block" in Columns, that will match to the colour it hits. In other puzzle-style games, like PopCorn, you have special powerups that do different things. ( Though it could be argued that PopCorn is more of an arcade game than a puzzle game )
4. Short average game length.
The time between starting a puzzle game, and finishing it, should not be too long. A few hours can be a long time for someone looking to "play a quick game." It should get difficult enough, fast enough, so that a game doesn''t last too long.
Now of course, I could have the wrong idea entirely about what you mean by a "puzzle game", Kevin
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Give me one more medicated peaceful moment.
~ (V)^|) |<é!t|-| ~
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