Step 1: Understanding the Concept:
We need to arrange the parts into a meaningful and grammatically correct sentence.
Step 2: Detailed Explanation:
The correct order is S-Q-P-R: "Some remarks casually dropped by a woman put the police on the right scent and they discovered the whole gang of brigands." S modifies "remarks", Q tells who made them, P shows the effect, and R gives the final result.
Step 3: Final Answer:
Thus, SQPR is the correct sequence.