The Collaborative International Dictionary of English v.0.48:

Insolvable \In*solv"a*ble\, a.
   1. Not solvable; insoluble; admitting no solution or
      explanation; as, an insolvable problem or difficulty. --I.
      Watts.
      [1913 Webster]

   2. Incapable of being paid or discharged, as debts.
      [1913 Webster]

   3. Not capable of being loosed or disentangled; inextricable.
      "Bands insolvable." --Pope.
      [1913 Webster]

WordNet (r) 3.0 (2006):

insolvable
    adj 1: not easily solved; "an apparantly insolvable problem";
           "public finance...had long presented problems unsolvable
           or at least unsolved"- C.L.Jones [syn: insolvable,
           unsoluble, unsolvable, unresolvable]