FindInstance
 Usage
• FindInstance[expr, vars] finds an instance of vars that makes the statement expr be True.
• FindInstance[expr, vars, dom] finds an instance over the domain dom. Common choices of dom are Complexes, Reals, Integers and Booleans.
• FindInstance[expr, vars, dom, n] finds n instances.
Notes
• FindInstance[expr, { ,  , ... }] gives results in the same form as Solve: {{ ->  ,  ->  , ... }} if an instance exists, and {} if it does not. • expr can contain equations, inequalities, domain specifications and quantifiers, in the same form as in Reduce. • With exact symbolic input, FindInstance gives exact results. • Even if two inputs define the same mathematical set, FindInstance may still pick different instances to return. • The instances returned by FindInstance typically correspond to special or interesting points in the set. • FindInstance[expr, vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex. • FindInstance[expr, vars, Integers] finds solutions to Diophantine equations. • FindInstance[expr, vars, Booleans] solves Boolean satisfiability for expr. • FindInstance[expr, vars, Reals] assumes that not only vars but also all function values in expr are real. FindInstance[expr && vars  Reals, vars] assumes only that the vars are real. • FindInstance may be able to find instances even if Reduce cannot give a complete reduction. • Every time you run FindInstance with a given input, it will return the same output. • Different settings for the option RandomSeed -> n may yield different collections of instances. • New in Version 5.
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