Question

Саша на доске записал натуральное трехзначное число зачеркивая поочередно каждую из цифр этого числа Саша на этой доске записал три двузначных числа сумма которых оказалась равной 168 Найдите трехзначное число Саши

Answer 1

я нахожу 2 таких числа 723 и 642

Answer 2

Finding the Three-Digit Number

To find the three-digit number that Sasha wrote on the board, we need to consider the three two-digit numbers whose sum is equal to 168.

Let's assume the three-digit number is represented as ABC, where A, B, and C are the digits of the number.

According to the given information, Sasha wrote three two-digit numbers by crossing out each digit of the three-digit number. Let's represent these two-digit numbers as XY, ZW, and UV, where X, Y, Z, W, U, and V are the digits of the two-digit numbers.

Based on this information, we can form the following equations:

Equation 1: X + Z + U = A Equation 2: Y + W + V = B Equation 3: X + Y + Z + W + U + V = C

We also know that the sum of the three two-digit numbers is equal to 168:

Equation 4: XY + ZW + UV = 168

Now, let's solve these equations to find the three-digit number Sasha wrote on the board.

Solving the Equations

To solve the equations, we can use trial and error or a systematic approach.

Let's start by considering all possible values for A, B, and C, which are the digits of the three-digit number.

Since the sum of the three two-digit numbers is 168, we can assume that A, B, and C are less than or equal to 16. This assumption helps us narrow down the possibilities and makes the calculation easier.

Let's consider the following values for A, B, and C:

A = 1, B = 6, C = 8 A = 2, B = 6, C = 8 A = 3, B = 6, C = 8 A = 4, B = 6, C = 8 A = 5, B = 6, C = 8 A = 6, B = 6, C = 8 A = 7, B = 6, C = 8 A = 8, B = 6, C = 8 A = 9, B = 6, C = 8

Now, let's substitute these values into the equations and check if we can find a solution.

For A = 1, B = 6, and C = 8, the equations become:

Equation 1: X + Z + U = 1 Equation 2: Y + W + V = 6 Equation 3: X + Y + Z + W + U + V = 8 Equation 4: XY + ZW + UV = 168

By solving these equations, we can find the values of X, Y, Z, W, U, and V, which will give us the three-digit number Sasha wrote on the board.

Unfortunately, without additional information or constraints, it is not possible to determine the exact three-digit number Sasha wrote on the board. The given information is not sufficient to uniquely determine the solution.

If you have any additional information or constraints, please provide them, and I will be happy to help you further.