Question

Количество цифр, потребовавшихся для нумерации страниц энциклопедии, не превосходит 2017. Если бы энциклопедия содержала на один лист больше, то количество цифр, потребовавшихся для нумерации страниц, превосходило бы 2017. Сколько листов в энциклопедии? А. 709 Б. 708 В. 355 Г. 354

Answer 1

А или В. Мне так кажется...

Answer 2

Solution

To solve this problem, we can use a simple algebraic equation. Let's denote the number of pages in the encyclopedia as x. According to the given information, the number of digits required to number the pages is less than or equal to 2017. If there were one more page, the number of digits required would exceed 2017.

Calculation

Let's set up the equation based on the given information:

1. The number of digits required to number the pages in the encyclopedia with x pages is given by the sum of the digits in the numbers from 1 to x. 2. The sum of the digits in the numbers from 1 to x can be calculated using the formula for the sum of the first n natural numbers: n(n+1)/2.

Using this information, we can set up the equation:

x(x+1)/2 ≤ 2017

Solving for x:

x(x+1) ≤ 4034

By trial and error, we find that the largest integer x that satisfies this inequality is 63. Therefore, the number of pages in the encyclopedia is 63.

Answer

So, the correct answer is: В. 355