Game Of Chords

What this combinatorial game-theory puzzle tests

This is a medium-difficulty puzzle that asks you to analyze a two-player combinatorial game with perfect information and no chance. Quant interviewers use questions like this to see whether you can move beyond brute-force game trees and spot structural patterns—symmetry, invariant moves, and winning/losing positions—that let you determine the outcome without computing every branch.

The setup is a concrete geometry problem: two players alternately draw non-crossing chords on a circle with a fixed set of points. The core skill being tested is backward induction and the ability to think about strategy stealing or pairing strategies—that is, whether one player can always respond to the opponent's move in a way that mirrors or neutralizes it, ensuring they never run out of legal moves.

• Symmetry and mirror strategies in combinatorial games
• Winning and losing positions under optimal play
• Non-crossing matchings and planar graph structure
• Parity and resource exhaustion

The problem explicitly asks for your reasoning, not just a yes-or-no answer. A strong response will identify which player benefits from the initial configuration and explain the strategic principle—such as a pairing strategy or a symmetry argument—that guarantees their win.