811 game

The 811 game is a simple yet engaging mathematical game where players take turns to subtract numbers from a starting total (often 811) until one player is forced to reach zero. Here's how it typically works: ### Rules of the 811 Game: 1. Starting Number: The game begins with a total of 811. 2. Players: Two players alternate turns. 3. Moves: On each turn, a player subtracts an integer from the current total. The integer must be: - A non-zero digit (19) or - A two-digit number (1099) that does not contain the digit '0' (e.g., 11, 23, but not 10 or 20). 4. Losing Condition: The player who reduces the total to exactly 0 wins. Alternatively, in some versions, the player forced to make the total negative loses. ### Example Gameplay: - Start: 811 - Player 1 subtracts 11 800 - Player 2 subtracts 8 792 - Player 1 subtracts 92 700 - Player 2 subtracts 7 693 - ... (game continues until one player reaches 0). ### Winning Strategy: The game is a variant of subtraction games (like Nim). To win, aim to leave your opponent with "losing positions" (totals where any move they make allows you to win). Key strategies include: - Forcing the total to multiples of 100 (e.g., 700, 600) by subtracting numbers like 11, 92, or other combos. - Avoiding leaving your opponent with flexible options (e.g., 811 - 11 = 800, which restricts their moves). ### Variations: - Different starting numbers (e.g., 100, 500). - Allowing subtraction of any 1- or 2-digit number (including those with 0, like 10 or 20). Would you like help analyzing a specific move or strategy?