Question

Саша и Костя по очереди вычеркивают по одной цифре из числа 179284 , пока не останется трехзначное число . Саша начинает , и его задача - сделать это трехзначное число как можно меньше. А Костя хочет , чтобы трехзначное число было как можно больше.Может ли Саша получить число меньше 295, как бы ни действовал Костя? Напишите свое решение.

Answer 1

Problem Analysis

In this problem, Sasha and Kostya take turns removing one digit from the number 179284 until a three-digit number remains. Sasha wants to minimize this three-digit number, while Kostya wants to maximize it. The question is whether Sasha can obtain a number smaller than 295, regardless of Kostya's actions.

Solution

To solve this problem, let's analyze the given number 179284 and the possible scenarios.

We start with the number 179284. Sasha's goal is to minimize the three-digit number, so he will try to remove the largest digits first. Kostya's goal is to maximize the three-digit number, so he will try to remove the smallest digits first.

Let's consider the possible scenarios:

1. Sasha removes the digit 9: The resulting number is 17284. 2. Kostya removes the digit 8: The resulting number is 1724. 3. Sasha removes the digit 7: The resulting number is 124. 4. Kostya removes the digit 4: The resulting number is 12.

At this point, only two digits remain, and the game ends. The resulting number is 12.

Since the resulting number is not a three-digit number, Sasha cannot obtain a number smaller than 295, regardless of Kostya's actions.

Therefore, the answer to the question is no, Sasha cannot obtain a number smaller than 295, no matter how Kostya acts.

Conclusion

In this problem, Sasha and Kostya take turns removing digits from the number 179284 until a three-digit number remains. Sasha wants to minimize the three-digit number, while Kostya wants to maximize it. Sasha cannot obtain a number smaller than 295, regardless of Kostya's actions.