Transversal achievement game on a square grid

TL;DR

This paper proves that the transversal achievement game on an n by n grid is always a draw for all n greater than 1, using mathematical induction and case analysis.

Contribution

It introduces a formal proof that the game results in a draw for all grid sizes greater than one, advancing understanding of this combinatorial game.

Findings

The game is a draw for all n > 1.

Mathematical induction confirms the hypothesis.

Case analysis supports the proof.

Abstract

This paper intends to solve the Transversal achievement on an n times n grid problem proposed by Dr. Martin Erickson. We approach the problem using mathematical induction and case analysis and prove the hypothesis that for all n greater than 1, the game is a draw.