1) Cryptic 2) Cryptical 3) Deep 4) Difficult to account for 5) French word used in English 6) Impenetrable 7) Impossible to solve 8) Incomprehensible 9) Indecipherable 10) Inscrutable 11) Insoluble 12) Mysterious 13) Mystifying 14) Not explicable 15) Paradoxical 16) Self-contradictory 17) Unaccountable 1) Cryptic 2) Cryptical 3) Enigmatic 4) Incomprehensible 5) Inexplainable 6) Inscrutable 7) Mysterious 8) Mystifying 9) Paradoxical 10) Strange 11) Unaccountable 12) Uncomprehensible 13) Unexplainable 14) Unintelligible 
• (a.) Not explicable; not explainable; incapable of being explained, interpreted, or accounted for; as, an inexplicable mystery.
In·ex'pli·ca·ble adjective [ Latin inexplicabilis : confer French inexplicable . See In- not, and Explicable .] Not explicable; not explainable; incapable of being explained, interpreted, or accounted for; as, an inexplicable mystery. 'An inexplicable scrat...
[adj] - incapable of being explained or accounted for
adjective incapable of being explained or accounted for; `inexplicable errors`; `left the house at three in the morning for inexplicable reasons`
not explicable; incapable of being accounted for or explained.