Question

На доске были написаны 10 последовательных натуральных чисел.Когда стёрли одно из них, то сумма девяти оставшихся оказалась равна 2002.Какие числа остались на доске

Answer 1

218 219 220 221 222 223 224 225 226 227

Cумма всех чисел:       S=(218+227)*10/2 =2225
Сумма оставшихся без 223:    2225 - 223 =2002

Answer 2

Problem Analysis

We are given that there were 10 consecutive natural numbers written on the board. When one of them was erased, the sum of the remaining nine numbers was equal to 2002. We need to find the numbers that were left on the board.

Solution

Let's assume that the first number on the board is x. Since the numbers are consecutive, the remaining numbers can be represented as x+1, x+2, ..., x+8, x+9. According to the problem, the sum of these nine numbers is equal to 2002.

To find the solution, we can set up the following equation:

x + (x+1) + (x+2) + ... + (x+8) + (x+9) = 2002

Simplifying the equation, we get:

9x + 45 = 2002

Solving for x, we find:

x = (2002 - 45) / 9 = 1957 / 9

Therefore, the first number on the board is approximately 217.

To find the remaining numbers, we can add 1 to 9 to the first number:

217, 218, 219, ..., 224, 225

So, the numbers that were left on the board are 217, 218, 219, 220, 221, 222, 223, 224, 225.

Answer

The numbers that were left on the board are 217, 218, 219, 220, 221, 222, 223, 224, 225.