problematical adj. 1. Posing a problem; difficult to solve. 2. Open to doubt; debatable. 3. Not settled; unresolved or dubious: a problematic future.

Life is not a problem to be solved, but a mystery to be lived. 
   -- Thomas Merton

abstract, abstruse, academic, ambiguous, analytical, apocryphal, arguable, as a premise, assumed, at issue, baffling, between rock and hard place, between sixes and sevens, betwixt and between, bewildering, bone of contention, borderline, chancy, clear as dishwater, clouded, codified, complex, complex, complicated, confounding, confusing, conjectural, contestable, contested, contingent, controversial, controvertible, cryptic, dark, debatable, deep, delicate, difficult, disinclined, disputable, doubtful, dubious, dubitable, effortful, elaborate, enigmatic, enigmatical, entangled, equivocal, esoteric, exceptionable, fishy, formalistic, formidable, formularized, general, Gordian, hard, hard to believe, hard to explain, hard to solve, hidden, hypothetical, ideal, idealized, ideational, ideological, iffy, imaginative, impractical, in dispute, in doubt, in question, in the abstract, in theory, inconclusive, indecisive, indefinite, indeterminate, inexplicable, inexplicit, instanced, intricate, involved, knotty, labyrinthine, logical, loose, mazy, meandering, metaphysical, mistrustful, moot, mootable, muddy, mysterious, mystical, mystifying, nodulous, notional, obscure, obstinate, occult, on paper, opaque, open, open to doubt, open to question, oracular, paradoxical, pedantic, perplexing, philosophical, postulated, precarious, presumed, problematic, profound, provisional, pure, questionable, quixotic, rambling, ramified, reticular, rough, rugged, shady, speculative, sticky*, subtle, suppositional, suspect, suspicious, tangled, tenebrous, tentative, terrible, the jury's out, thorny, ticklish, touch and go, tough, transcendent, transcendental, tricky, troublesome, uncertain, unclear, unconfirmed, undefined, under advisement, under examination, unearthly, unfathomable, unintelligible, unproved, unproven, unreliable, unsettled, unsubstantiated, unsure, up for discussion, up for grabs, uphill, vague, vexing. 

-- Roget's 21st Century Thesaurus

Conversely, when one writes or speaks the word problematical, one might well be advised to use one of those ten senses explicitly to avoid confusing one's reader or listener.  Then too, almost certainly, one of problematical's 200 synonyms will work better.

One problem with the word problematical is the embedded word problem.  As I have written elsewhere, some people are troubled by the use of the word problem in various contexts.  Often the word problem need not signify trouble.

Finally, there are the pleasant aspects of problem-solving, which are accommodated most commonly by substituting the word puzzle, as explored throughout Puzzles with a Purpose.

Despite all of its senses and synonyms, the word problematical does not seem to make room for recreation, a lament footnoted at The Puzzle as a Literary Genre.