Here is a 3-paragraph summary of the blog post for mathopen.com:
The Round Table Coin Game is a classic two-player puzzle that has been used as a teaching tool in math classes for years. The setup is simple: two players take turns placing quarters on a round table, with each coin needing to fit entirely on the table without overlapping any previously placed coin. The player who cannot find a valid spot to place their next quarter loses the game.
What makes this puzzle so fascinating is that one of the two players has a guaranteed winning strategy, no matter how their opponent plays. The first player can always win by placing the very first quarter at the exact center of the table. From that point on, whatever move the second player makes, the first player mirrors it symmetrically through the center point. This strategy ensures that whenever the second player has a valid move available, the first player will always have a corresponding mirror move available as well.
The beauty of this puzzle lies in its elegant use of symmetry as a mathematical weapon. The mirroring strategy guarantees that the second player will always be the first one unable to move, handing the victory to the first player every time. This type of reasoning, known as a strategy-stealing argument, appears throughout combinatorial game theory and serves as a wonderful entry point for students exploring mathematical thinking and proof strategies.