Question

Незнайка написал число 31 потом приписал к нему слева это же число задом наперед получилось 3113 с полученным 4 - значным числом он снова повторил эту операцию стало 31133113 и так 10 раз подряд найдите остаток от деления на 9 у получившегося числа

Answer 1

Вот этот ответ повтори 10 раз,а остаток получается 8 всё равно

Answer 2

Solution:

To find the remainder of the division by 9 of the resulting number after the given operations, we can follow these steps:

1. Initial Number: The initial number is 31. 2. Operation 1: Concatenate the initial number with its reverse (31 + 13 = 3113). 3. Operation 2: Concatenate the result of Operation 1 with its reverse (3113 + 3113 = 31133113). 4. Repeat Operation: Repeat the second step 10 times.

Let's calculate the result step by step and find the remainder of the final number after each operation.

Step-by-Step Calculation:

1. Initial Number: 31 2. Operation 1: Concatenate 31 with its reverse: 31 + 13 = 3113 3. Operation 2: Concatenate 3113 with its reverse: 3113 + 3113 = 31133113 4. Operation 3: Concatenate 31133113 with its reverse: 31133113 + 31133113 = 31133113311313 5. Operation 4: Concatenate 31133113311313 with its reverse: 31133113311313 + 31133113311313 = 3113311331131331133113 6. Operation 5: Concatenate 3113311331131331133113 with its reverse: 3113311331131331133113 + 3113311331131331133113 = 3113311331131331133113311331133113 7. Operation 6: Concatenate 3113311331131331133113311331133113 with its reverse: 3113311331131331133113311331133113 + 3113311331131331133113311331133113 = 3113311331131331133113311331133113311331131331133113 8. Operation 7: Concatenate 3113311331131331133113311331133113311331131331133113 with its reverse: 3113311331131331133113311331133113311331131331133113 + 3113311331131331133113311331133113311331131331133113 = 3113311331131331133113311331133113311331131331133113311331131331133113 9. Operation 8: Concatenate 3113311331131331133113311331133113311331131331133113311331131331133113 with its reverse: 3113311331131331133113311331133113311331131331133113311331131331133113 + 3113311331131331133113311331133113311331131331133113311331131331133113 = 3113311331131331133113311331133113311331131331133113311331131331133113311331131331133113 10. Operation 9: Concatenate 3113311331131331133113311331133113311331131331133113311331131331133113311331131331133113 with its reverse: 3113311331131331133113311331133113311331131331133113311331131331133113311331131331133113 + 3113311331131331133113311331133113311331131331133113311331131331133113311331131331133113 = 3113311331131331133113311331133113311331131331133113311331131331133113311331131331133113311331131331133113311331131331133113

Result:

The final number after 10 operations is 3113311331131331133113311331133113311331131331133113311331131331133113311331131331133113311331131331133113311331131331133113.

To find the remainder of the division by 9 of this number, we can calculate the sum of its digits and find the remainder of that sum divided by 9.

Calculating the Sum of Digits:

3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 + 1 + 1 + 3 + 3 +