This talk delves into the mathematical solving of an 1D impartial avoidance game we named "Inverse Treblecross", adapted from the game "Treblecross" introduced by Berlekamp, Conway and Guy in their famous work "Winning Ways for Your Mathematical Plays". For audiences new to Combinatorial Game Theory, the presentation will begin with a gentle introduction to the Sprague-Grundy (SG) theorem and octal games. We will see how standard games neatly decompose into independent subgames. However, Inverse Treblecross is notoriously stubborn: placing a piece does not cleanly isolate the remaining empty spaces, making it remarkably difficult to evaluate.

Despite this resistance, we reveal a surprising hidden order. By constructing specific characteristic functions and mapping board parities, we demonstrate that the SG sequence for an empty board is ultimately confined to the values 0 and 1, perfectly dictated by a modulo-10 rule.

In general, the topic of combinatorial game theory also plays an important role in mathematics education. I will conclude the talk by sharing how relevant topics originated and evolved through teaching practices. No prior knowledge of Combinatorial Game Theory is required. The talk will be self-contained and accessible to a general math audience.