Hard-working students

What this set-theory puzzle tests

This is an easy combinatorics puzzle that appears frequently in quant-interview warm-ups. It tests whether you can apply the inclusion-exclusion principle to recover information about overlapping groups from aggregate counts.

The problem gives you the sizes of three sets and their pairwise intersections, and asks you to infer a specific subset—those elements belonging to exactly one set. The skill being tested is comfort with Venn diagram logic and the ability to systematically partition a universe into mutually exclusive regions.

• Inclusion-exclusion principle
• Venn diagram partitioning
• Reasoning about set complements and intersections