The most basic requirement of successful use of trial and error is all too often forgotten - you must keep track of what you have tried.
Systemic trial and error is based on a mutually exclusive and exhaustive listing of all possible solutions. In many real world problems this isn't possible, but it works in some areas such as mathematics and some areas of engineering. Even just attempting an exhaustive listing of solutions can help you find possible solutions that you may have overlooked otherwise, even if a truly exhausitve listing is not possible.
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