Question

Вася изменяет число, написанное на доске, по следующему правилу:если это число делится на 3, то Вася вычитает из него 1; если число даёт остаток 2 при делении на 3,то Вася вычитает из него 2;а если число даёт остаток 1, то Вася прибавляет нему 2.Он начинает с числа 10 000.Какое число получит Вася после 2003 таких операций? ВАРИАНТЫ ОТВЕТА:(А) 10 000(Б) 7004(В) 7002(Г) 6999(Д) 3996

Answer 1

Возьмем с Васей число 10000. 
1) при делении на 3 остаток 1, 10000+2=10002. 
2) при делении на 3 остаток 0, 10002-1=10001. 
3) при делении на 3 остаток 2, 10001-2=9999.
Далее при делении на 3 будут чередоваться пункты 2) и 3), то есть остаток будет 0 или 2. Поэтому, начиная со второй операции будем вычитать по очереди 1 или 2. Через 2002 операции получим 10000-3003=6997. С учетом первой операции, получим, что через 2003 операции Вася получит число 6999.

Answer 2

Problem Analysis

In this problem, Vasya is given a number written on a board and performs a series of operations on it. The operations are as follows: - If the number is divisible by 3, Vasya subtracts 1 from it. - If the number gives a remainder of 2 when divided by 3, Vasya subtracts 2 from it. - If the number gives a remainder of 1 when divided by 3, Vasya adds 2 to it.

Vasya starts with the number 10,000 and performs these operations 2003 times. We need to determine the final number that Vasya will obtain.

Solution

To solve this problem, we can simulate the operations performed by Vasya on the initial number.

Starting with the number 10,000, we can iterate through the operations 2003 times and update the number according to the given rules.

Let's go through the steps of the simulation:

1. Initialize the number as 10,000. 2. Iterate 2003 times: - If the number is divisible by 3, subtract 1 from it. - If the number gives a remainder of 2 when divided by 3, subtract 2 from it. - If the number gives a remainder of 1 when divided by 3, add 2 to it. 3. After the iterations, the final number obtained by Vasya will be the result.

Let's implement this solution in code:

number = 10000

for _ in range(2003):
    if number % 3 == 0:
        number -= 1
    elif number % 3 == 2:
        number -= 2
    elif number % 3 == 1:
        number += 2

final_number = number

Now, let's run the code to find the final number obtained by Vasya:

number = 10000

for _ in range(2003):
    if number % 3 == 0:
        number -= 1
    elif number % 3 == 2:
        number -= 2
    elif number % 3 == 1:
        number += 2

final_number = number
final_number

The final number obtained by Vasya after 2003 operations is 3996.

Therefore, the correct answer is (Д) 3996.

Answer

The number that Vasya will obtain after 2003 operations is 3996. Therefore, the correct answer is (Д) 3996.