1817, "trackless," from clue (n.) + -less. Meaning "ignorant, uninformed" is by 1943, said to be RAF slang from 1930s. Student slang use by 1985 is perhaps an independent extension along the same line. Related: Cluelessly; cluelessness.
club-foot
club-house
club-moss
cluck
clue
clueless
clump
clumperton
clumpy
clumsy
clung