Chapter 1: Introduction to the Game

Mathematics often gets a reputation for being tedious, particularly when preparing for an exam that looms just a month away. However, when we incorporate math into a game, it transforms into an engaging experience.

Here’s how the game unfolds: Players A and B take turns writing a positive integer on the board, with the condition that no player can write a number that is a factor of any previously written number. Player A begins the game.

The intriguing twist is that Player A can secure a win every time if they start first.

So, how does this work?

I suggest you take a moment to pause here, grab a pen and paper, and try this out for yourself.

Chapter 2: The Fascinating Role of the Number 1

Math can indeed be enjoyable! One of the most fascinating aspects of this game is the significance of the number 1. For any chosen positive integer n, we can analyze the situation by excluding the number 1. For the range of numbers from 2 to n, either the first player has a winning strategy, or the second player does.

If the first player can win, then for any set of numbers from 1 to n, Player A can replicate that winning strategy. Conversely, if the second player has the advantage, Player A can start by writing down 1, thereby shifting the scenario to one where the second player is likely to win.

For instance, let’s consider n=10. Player A can start by writing 6, which leaves the numbers 4, 5, 7, 8, 9, and 10 available for Player B. These six numbers can be categorized into three pairs: (4, 5), (7, 9), and (8, 10). Regardless of the number Player B selects, Player A can always choose the complementary number within the same pair (e.g., if Player B writes 4, Player A will write 5). This strategy enables Player A to ensure they will be the last to write a number.

Isn’t that fascinating? Invite a friend to join you and test this strategy!

Chapter 3: Video Insights into the Game

The first video, A Game You Can Always Win, delves into the principles behind winning strategies in this math game. It provides insights that can enhance your understanding and approach.

The second video, Win this game EVERY time using math!, offers effective techniques and strategies that ensure victory every time you engage in this game.

Thank you for engaging with this content! Enjoy your game-playing experience!