Question

Играют двое . Первый игрок называет любое число но не выше 10 . Второй прибовляет к названаму числу число не выше 10 и сообщает сумму . 1-й к этой сумме он прибовляет число но не меньше 10 и т.д. до тех пор , пока ок. Суммой не окажется 100.Выигравает тот , кто первым достигает 100. Как должен действовать первый игрок , чтобы выйграть .

Answer 1

Первый игрок побеждает в любом случае
По действиям:
1. (<=10) x; Напр 3.
2. (<=10) y; Напр 7.

(x+y)<=20; Напр 10.
1. (>=10) Отвечает числом 100-(x+y) - Число от 80 до 100. Напр 100 - 10 = 90.

Answer 2

Rules of the Game

In this game, two players take turns adding numbers to a running total. The first player starts by naming any number between 1 and 10 (inclusive). The second player then adds a number between 1 and 10 to the running total and announces the sum. The first player then adds a number between 10 and the current sum (inclusive) to the running total, and the game continues in this manner until the running total reaches 100. The player who reaches 100 first wins the game.

Strategy for the First Player

To determine the strategy for the first player to win the game, we need to consider the possible scenarios and outcomes. Let's analyze the game step by step:

1. The first player starts by naming a number between 1 and 10 (inclusive). 2. The second player adds a number between 1 and 10 to the running total and announces the sum. 3. The first player adds a number between 10 and the current sum (inclusive) to the running total.

To maximize their chances of winning, the first player should aim to reach a multiple of 11 (11, 22, 33, etc.) on their turn. This is because the second player will always be forced to add a number between 1 and 10, and the sum will always be a multiple of 11 plus a number between 1 and 10. By following this strategy, the first player can ensure that the running total remains a multiple of 11 throughout the game.

For example, if the first player starts with the number 1, the second player will add a number between 1 and 10, resulting in a sum between 2 and 11. The first player can then add a number between 10 and the current sum (inclusive) to reach a multiple of 11. This pattern continues, with the first player always aiming to reach a multiple of 11 on their turn.

By consistently following this strategy, the first player can control the running total and force the second player into a disadvantageous position. This gives the first player a higher chance of reaching 100 first and winning the game.

To summarize, the first player should aim to reach a multiple of 11 on their turn to maximize their chances of winning the game.

I hope this helps! Let me know if you have any further questions.