Question

Первого сентября директор сказал первоклассникам, что в школе обучается примерно 1000 учеников, и предложил ребятам угадать точное количество. Артём сказал 990, Боря — 999, Витя — 1001, Гоша — 1005, а Дима — 1010. Тогда учитель сказал, что точно не угадал никто, а ошибки были такими: 2, 4, 7, 8 и 13 (возможно, в другом порядке). Сколько в школе учеников?

Answer 1

В школе 997 учеников.
тогда Артём ошибся на 7, Боря на 2, Витя на 4, Гоша на 8, Дима на 13.

Answer 2

Calculating the Number of Students in the School

To calculate the number of students in the school, we can use the information provided by the teacher and the students' guesses.

The teacher mentioned that there are approximately 1000 students in the school and asked the students to guess the exact number. The students' guesses were as follows: - Artyom: 990 - Boris: 999 - Vitya: 1001 - Gosha: 1005 - Dima: 1010

The teacher then revealed that none of the students guessed the exact number, and the errors were as follows: 2, 4, 7, 8, and 13 (in some order).

Calculating the Exact Number of Students

To calculate the exact number of students, we can analyze the errors provided by the teacher and the students' guesses.

The errors provided by the teacher are 2, 4, 7, 8, and 13. By comparing these errors with the students' guesses, we can determine the correct number of students in the school.

- Artyom: 990 (error: 10) - Boris: 999 (error: 1) - Vitya: 1001 (error: 1) - Gosha: 1005 (error: 5) - Dima: 1010 (error: 10)

By analyzing the errors, we can see that the errors correspond to the differences between the students' guesses and the actual number of students. Therefore, we can calculate the exact number of students by finding the number that, when adjusted by the errors, matches the students' guesses.

Calculating the Exact Number of Students

Let's denote the exact number of students as x. Then, we can form the following equations based on the students' guesses and the errors provided by the teacher:

- Artyom: x - 10 = 990 - Boris: x - 1 = 999 - Vitya: x - 1 = 1001 - Gosha: x - 5 = 1005 - Dima: x - 10 = 1010

Solving these equations will give us the exact number of students in the school.

Solving the Equations

Solving the equations: - Artyom: x - 10 = 990 => x = 990 + 10 = 1000 - Boris: x - 1 = 999 => x = 999 + 1 = 1000 - Vitya: x - 1 = 1001 => x = 1001 + 1 = 1002 - Gosha: x - 5 = 1005 => x = 1005 + 5 = 1010 - Dima: x - 10 = 1010 => x = 1010 + 10 = 1020

By analyzing the solutions, we can see that the only number that satisfies all the students' guesses and the errors provided by the teacher is 1000.

Therefore, the exact number of students in the school is 1000.