The Collaborative International Dictionary of English v.0.48:

Solid \Sol"id\ (s[o^]l"[i^]d), a. [L. solidus, probably akin to
   sollus whole, entire, Gr. ???: cf. F. solide. Cf.
   Consolidate,Soda, Solder, Soldier, Solemn.]
   1. Having the constituent parts so compact, or so firmly
      adhering, as to resist the impression or penetration of
      other bodies; having a fixed form; hard; firm; compact; --
      opposed to fluid and liquid or to plastic, like
      clay, or to incompact, like sand.
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   2. Not hollow; full of matter; as, a solid globe or cone, as
      distinguished from a hollow one; not spongy; dense;
      hence, sometimes, heavy.
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   3. (Arith.) Having all the geometrical dimensions; cubic; as,
      a solid foot contains 1,728 solid inches.
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   Note: In this sense, cubics now generally used.
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   4. Firm; compact; strong; stable; unyielding; as, a solid
      pier; a solid pile; a solid wall.
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   5. Applied to a compound word whose parts are closely united
      and form an unbroken word; -- opposed to hyphened.
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   6. Fig.: Worthy of credit, trust, or esteem; substantial, as
      opposed to frivolous or fallacious; weighty; firm;
      strong; valid; just; genuine.
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            The solid purpose of a sincere and virtuous answer.
                                                  --Milton.
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            These, wanting wit, affect gravity, and go by the
            name of solid men.                    --Dryden.
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            The genius of the Italians wrought by solid toil
            what the myth-making imagination of the Germans had
            projected in a poem.                  --J. A.
                                                  Symonds.
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   7. Sound; not weakly; as, a solid constitution of body. --I.
      Watts.
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   8. (Bot.) Of a fleshy, uniform, undivided substance, as a
      bulb or root; not spongy or hollow within, as a stem.
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   9. (Metaph.) Impenetrable; resisting or excluding any other
      material particle or atom from any given portion of space;
      -- applied to the supposed ultimate particles of matter.
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   10. (Print.) Not having the lines separated by leads; not
       open.
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   11. United; without division; unanimous; as, the delegation
       is solid for a candidate. [Polit. Cant. U.S.]
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   Solid angle. (Geom.) See under Angle.

   Solid color, an even color; one not shaded or variegated.


   Solid green. See Emerald green
       (a), under Green.

   Solid measure (Arith.), a measure for volumes, in which the
      units are each a cube of fixed linear magnitude, as a
      cubic foot, yard, or the like; thus, a foot, in solid
      measure, or a solid foot, contains 1,728 solid inches.

   Solid newel (Arch.), a newel into which the ends of winding
      stairs are built, in distinction from a hollow newel. See
      under Hollow, a.

   Solid problem (Geom.), a problem which can be construed
      geometrically, only by the intersection of a circle and a
      conic section or of two conic sections. --Hutton.

   Solid square (Mil.), a square body or troops in which the
      ranks and files are equal.
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   Syn: Hard; firm; compact; strong; substantial; stable; sound;
        real; valid; true; just; weighty; profound; grave;
        important.

   Usage: Solid, Hard. These words both relate to the
          internal constitution of bodies; but hardnotes a more
          impenetrable nature or a firmer adherence of the
          component parts than solid. Hard is opposed to soft,
          and solid to fluid, liquid, open, or hollow. Wood is
          usually solid; but some kinds of wood are hard, and
          others are soft.
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                Repose you there; while I [return] to this hard
                house,
                More harder than the stones whereof 't is
                raised.                           --Shak.
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                I hear his thundering voice resound,
                And trampling feet than shake the solid ground.
                                                  --Dryden.
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The Collaborative International Dictionary of English v.0.48:

Problem \Prob"lem\, n. [F. probl[`e]me, L. problema, fr. Gr. ?
   anything thrown forward, a question proposed for solution,
   fr. ? to throw or lay before; ? before, forward + ? to throw.
   Cf. Parable. ]
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   1. A question proposed for solution; a matter stated for
      examination or proof; hence, a matter difficult of
      solution or settlement; a doubtful case; a question
      involving doubt. --Bacon.
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   2. (Math.) Anything which is required to be done; as, in
      geometry, to bisect a line, to draw a perpendicular; or,
      in algebra, to find an unknown quantity.
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   Note: Problem differs from theorem in this, that a problem is
         something to be done, as to bisect a triangle, to
         describe a circle, etc.; a theorem is something to be
         proved, as that all the angles of a triangle are equal
         to two right angles.
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   Plane problem (Geom.), a problem that can be solved by the
      use of the rule and compass.

   Solid problem (Geom.), a problem requiring in its geometric
      solution the use of a conic section or higher curve.
      [1913 Webster] Problematic