Question

На доске записали трёхзначное число которое начиналось цифрой 9. Юрик переставил эту 9 на последнее место, в результате данное число получилось на 216 меньше данного. Какое число было написано на доске?

Answer 1

975-759=216

ответ: 975

Answer 2

Problem Analysis

We are given a three-digit number that starts with the digit 9. Yuri rearranges the 9 to the last position, resulting in a number that is 216 less than the original number. We need to determine the original number.

Solution

Let's consider the original number as ABC, where A, B, and C represent the digits of the number. Since the number starts with 9, we have A = 9.

After Yuri rearranges the digits, the new number becomes BCA. According to the problem, this new number is 216 less than the original number. Mathematically, we can represent this as:

100 \* B + 10 \* C + A = 100 \* A + 10 \* B + C - 216

Simplifying the equation, we get:

100B + 10C + 9 = 900 + 10B + C - 216

Combining like terms, we have:

90B + 9C = 693

Dividing both sides of the equation by 9, we get:

10B + C = 77

Since we know that A = 9, the original number is 9BC. From the equation above, we can see that B + C = 7. Therefore, the possible values for B and C are (1, 6), (2, 5), (3, 4), or (4, 3).

Let's check each possibility to find the original number:

1. If B = 1 and C = 6, the original number is 916. However, this does not satisfy the condition that the number starts with 9. 2. If B