Question

На калькуляторе вбито число 1. Петя и Вася по очереди делают следующие операции: Петя прибавляет или вычитает 3, Вася умножает на 2 или на 4. Могут ли они получит а)1000,б)500 если первую операцию делает Петя? Даю 20 баллов :)

Answer 1

1000 получат ᅠ ᅠᅠ ᅠᅠ ᅠ

ᅠ ᅠᅠ ᅠᅠ ᅠ

Answer 2

Problem Analysis

Petya and Vasya are performing operations on a calculator. Petya adds or subtracts 3, while Vasya multiplies by 2 or 4. The initial number on the calculator is 1. We need to determine if they can obtain the numbers 1000 and 500, respectively, if Petya performs the first operation.

Solution

To solve this problem, we can simulate the operations performed by Petya and Vasya and check if the desired numbers can be obtained.

Let's start with the first case: Can they obtain the number 1000?

Case 1: Obtaining 1000

If Petya performs the first operation, we need to determine if it is possible to reach 1000 by adding or subtracting 3, and then multiplying by 2 or 4.

Let's analyze the possible sequences of operations:

1. Petya adds 3, resulting in 4. Vasya multiplies by 2, resulting in 8. Vasya multiplies by 2 again, resulting in 16. Vasya multiplies by 2 again, resulting in 32. Vasya multiplies by 2 again, resulting in 64. Vasya multiplies by 2 again, resulting in 128. Vasya multiplies by 2 again, resulting in 256. Vasya multiplies by 2 again, resulting in 512. Vasya multiplies by 2 again, resulting in 1024. The number 1000 cannot be obtained.

2. Petya adds 3, resulting in 4. Vasya multiplies by 2, resulting in 8. Vasya multiplies by 2 again, resulting in 16. Vasya multiplies by 2 again, resulting in 32. Vasya multiplies by 2 again, resulting in 64. Vasya multiplies by 2 again, resulting in 128. Vasya multiplies by 2 again, resulting in 256. Vasya multiplies by 2 again, resulting in 512. Vasya multiplies by 4, resulting in 2048. The number 1000 cannot be obtained.

3. Petya adds 3, resulting in 4. Vasya multi