Questions: 25. Game-Optional. Play the game below on the grid that appears on the following page. The first player places a piece in any of the spaces. The second player may play in any space, but if the second player places a piece next to one that is on the board, it must be different from that piece in two ways. Can you fill up the board? To make this game competitive, you may divide the pieces at random and require each player to draw from his or her own group of pieces. To further increase the challenge, play with only the large pieces or the small pieces. Make up some new rules for the game. For example, you may vary the number of differences required.

The question describes a game involving placing pieces on a grid with specific rules about how the pieces can be placed relative to each other. Here’s a step-by-step breakdown of the game and how to approach it:

1. Understanding the Game Rules:

   • The first player can place a piece in any space on the grid.
   • The second player can place a piece in any space, but if the piece is placed next to an existing piece, it must differ in two ways from the adjacent piece.

2. Objective:

   • The goal is to fill up the board following these rules.

3. Making the Game Competitive:

   • Divide the pieces randomly between the players.
   • Each player draws from their own set of pieces.

4. Increasing the Challenge:

   • Play with only large pieces or only small pieces.
   • Introduce new rules, such as varying the number of differences required between adjacent pieces.

5. Example of New Rules:

   • You could require that adjacent pieces differ in three ways instead of two.
   • You could introduce a rule where pieces must differ in color, shape, and size.

6. Strategy for Filling the Board:

   • Start by placing a piece in a central location to maximize the number of options for the second player.
   • Plan ahead to ensure that each new piece placed allows for future moves that comply with the rules.

7. Example Moves:

   • If the first player places a red, large, circular piece in the center, the second player could place a blue, small, square piece next to it, as it differs in color, size, and shape.

By following these guidelines and strategies, players can engage in a competitive and challenging game while adhering to the rules provided.