I haven't got a clue
Without any knowledge or understanding.
This little phrase, which is often given as 'I don't have a clue', doesn't at first sight appear to be idiomatic at all and hardly deserving of investigation. After all, a clue is an insight or idea that points us towards a solution. To be without a clue is simply to be ignorant. However, a clue (also spelled clew) previously had a different meaning - a globular ball formed from coiling worms or the like or, more specifically, a ball of thread. Clew has been used with that meaning for at least a thousand years and citations of it in Old English date back to 897AD, when no less an author than Aelfred, King of Wessex used it in his West-Saxon translation of Gregory's Pastoral Care. Shakespeare also used the word with the 'thread' meaning, for example, in All's Well that Ends Well, 1602:
"If it be so, you have wound a goodly clewe."
That seems a long way from crossword clues or Sherlock Holmes' stories. How did we get from a ball of thread to the current meaning of clue?
Go back to Greek myth and recall the tale of Theseus and the Minotaur. Theseus entered the labyrinth to kill the half-man, half-bull Minotaur. He did so but was only able to find his way out by retracing his path, marked by the string given to him by Ariadne. So, Theseus 'had a clew' about the safe route out of the maze and was able to escape.
Geoffrey Chaucer recorded this story in The Legend of Ariadne, Part VI of The Legend of Good Women, 1385:
Therto have I a remedie in my thoght,
By a clewe of twyn as he hath gon,
The same weye he may returne a-non,
ffolwynge alwey the thred as he hath come.
So, don't be clueless - all you need is some string.