Strange 20-gon

What this combinatorial labelling puzzle tests

This is an easy combinatorial puzzle that appears in quant interview loops to assess how you approach constraint-satisfaction problems. You are given a concrete geometric structure—a polygon with a specific number of vertices—and must find a property that holds under a set of labelling rules.

The puzzle rewards clear logical reasoning: once you understand the constraints (adjacency rules and label range), the answer follows from a structural insight rather than brute-force enumeration. The key is recognizing what the constraints force to be true, rather than trying to construct an explicit solution.

• Parity and cycle structure
• Constraint propagation
• Invariants under permutations