Question

Толя читал книгу и запомнил номер страницы, где остановился. это трехзначное число, причем все цифры этого числа различны. Толя точно знает, что каждая следующая цифра этого делиться без остатка на предыдущую, первая цифра этого числа четная, а последняя цифра не является нулем. на какой станице остановился толя? найдите номер станицы и объясните как вы его нашли.

Answer 1

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Answer 2

Finding the Page Number

To find the page number where Tolya stopped reading, we need to consider the given conditions: 1. The page number is a three-digit number. 2. All the digits in the number are different. 3. Each subsequent digit is divisible by the previous digit without a remainder. 4. The first digit is even. 5. The last digit is not zero.

Let's go through the conditions step by step to find the page number.

1. The first condition states that the page number is a three-digit number. This means the number is between 100 and 999.

2. The second condition states that all the digits in the number are different. This means we need to find a three-digit number with three distinct digits.

3. The third condition states that each subsequent digit is divisible by the previous digit without a remainder. This means the second digit should be divisible by the first digit, and the third digit should be divisible by the second digit.

4. The fourth condition states that the first digit is even. This means the first digit can be 2, 4, 6, or 8.

5. The fifth condition states that the last digit is not zero. This means the last digit can be any digit from 1 to 9.

Now, let's find the page number that satisfies all these conditions.

Finding the Page Number: Step by Step

1. We start with the first condition, which states that the page number is a three-digit number. This means the number is between 100 and 999.

2. Next, we consider the fourth condition, which states that the first digit is even. This means the first digit can be 2, 4, 6, or 8.

3. Now, let's consider the second condition, which states that all the digits in the number are different. We can start by trying different combinations of the remaining two digits (excluding the first digit) and check if they satisfy the third condition.

- If we choose the second digit as 1, the third digit can be 2, 3, 4, 5, 6, 7, 8, or 9. However, none of these combinations satisfy the third condition. - If we choose the second digit as 3, the third digit can be 6 or 9. However, none of these combinations satisfy the third condition. - If we choose the second digit as 5, the third digit can be 0 or 5. However, none of these combinations satisfy the third condition. - If we choose the second digit as 7, the third digit can be 4. This combination satisfies the third condition.

Therefore, the possible combinations for the second and third digits are 74.

4. Now, let's consider the fifth condition, which states that the last digit is not zero. This means the last digit can be 4.

5. Combining the first, fourth, and fifth conditions, we find that the possible page numbers are 274 and 874.

Therefore, Tolya could have stopped reading on either page 274 or page 874.

Explanation of the Solution

To find the page number where Tolya stopped reading, we considered the given conditions step by step. By analyzing the conditions and trying different combinations of digits, we found that the possible page numbers are 274 and 874.

Please note that the given information does not provide a unique solution for the page number where Tolya stopped reading. There could be other possible page numbers that satisfy the given conditions.