One of our question setters heard this question as a child, but unfortunately did not hear the answer. And you know what quizzers are like - this gnawed away for years until he finally worked out the answer.
So the question . . .
How can a bowler in a cricket match take a hat trick and take each of the three wickets in different overs?
The bowler takes the first wicket with the sixth and final ball of an over.
Then the bowler takes the second wicket with the first ball of their next over, which is also the tenth and final wicket of the opposition's first innings.
Finally, the bowler takes the third wicket with the first ball of their first over in the second innings.
And yes, this does count as a hat trick!
Indeed, in 1988 Merv Hughes playing for Australia against the West Indies did this.