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While answering Trouble getting FindInstance to return multiple results for certain constraints it became clear that for this problem FindInstance would be better starting with small numbers, but it does not.

The function has the Method option:

Options[FindInstance, Method]   (*  Out: {Method -> Automatic}  *)

Yet, I cannot find documentation for the methods (and methods sub-options) that it accepts.

  • What Method values does FindInstance accept?
  • Will any of them scan an Integer search space small-values first?
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A perusal of ??System`InstanceDump`* might provide a few clues, I think. –  J. M. Jun 14 '12 at 12:43
    
Related> Here there are a few options for FindInstance[] mentioned reference.wolfram.com/mathematica/tutorial/… –  belisarius Jun 14 '12 at 12:59
    
@J.M. that command yields Information::nomatch: No symbol matching System`InstanceDump`* found. >> on my system. –  Mr.Wizard Jun 14 '12 at 13:13
    
@belisarius I see the low-level (and wide effect) SystemOptions, but not Method options. Am I overlooking something? –  Mr.Wizard Jun 14 '12 at 13:13
    
Ech, I keep forgetting that you're on version seven... –  J. M. Jun 14 '12 at 13:14
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