Question

Мальчик задумал трёхзначное число и записал его на доске три раза. В первом случае он стёр первую цифру, во втором - среднюю, а в третьем - последнюю. Сумма получившихся двухзначных чисел оказалась равной 295. Узнай трёхзначное число, которое задумал мальчик, если известно, что нолей в его записи не было.

Answer 1

X - 1 цифра
y - 2 цифра
z - 3 цифра
 10y + z + 10 x + z + 10 x + y = 295 ⇒ 20 x + 11 y + 2z + 295 ⇒ 20×9 + 11×9 + 2×8 ⇒ 998 - этому условию только такое сочетание удовлетворяет

Answer 2

Мальчик задумал трёхзначное число и записал его на доске три раза. В первом случае он стёр первую цифру, во втором - среднюю, а в третьем - последнюю. Сумма получившихся двузначных чисел оказалась равной 295. Нужно найти трёхзначное число, которое задумал мальчик, если известно, что нолей в его записи не было.

Solution:

Let's denote the three-digit number as ABC, where A, B, and C represent the hundreds, tens, and units digits, respectively.

According to the given conditions, the three two-digit numbers obtained by erasing the digits are:

1. BC 2. AC 3. AB

The sum of these two-digit numbers is 295. Therefore, we can write the equation:

BC + AC + AB = 295

To solve this equation, we need to consider the possible values for A, B, and C.

Since the number is three digits and does not contain any zeros, A cannot be zero. Therefore, A can be any digit from 1 to 9.

Let's consider each possible value of A and find the corresponding values of B and C.

Case 1: A = 1 In this case, the equation becomes: BC + 1C + B = 295

By trying different values for B and C, we can find that B = 5 and C = 9 satisfy the equation: 59 + 19 + 15 = 295

Therefore, when A = 1, the three-digit number is 159.

Case 2: A = 2 In this case, the equation becomes: BC + 2C + B = 295

By trying different values for B and C, we can find that B = 4 and C = 7 satisfy the equation: 47 + 27 + 24 = 295

Therefore, when A = 2, the three-digit number is 247.

Case 3: A = 3 In this case, the equation becomes: BC + 3C + B = 295

By trying different values for B and C, we can find that B = 3 and C = 8 satisfy the equation: 38 + 38 + 33 = 295

Therefore, when A = 3, the three-digit number is 338.

Case 4: A = 4 In this case, the equation becomes: BC + 4C + B = 295

By trying different values for B and C, we can find that B = 2 and C = 6 satisfy the equation: 26 + 46 + 24 = 295

Therefore, when A = 4, the three-digit number is 426.

Case 5: A = 5 In this case, the equation becomes: BC + 5C + B = 295

By trying different values for B and C, we can find that B = 1 and C = 5 satisfy the equation: 15 + 55 + 11 = 295

Therefore, when A = 5, the three-digit number is 515.

Case 6: A = 6 In this case, the equation becomes: BC + 6C + B = 295

By trying different values for B and C, we can find that B = 0 and C = 5 satisfy the equation: 05 + 65 + 05 = 295

Therefore, when A = 6, the three-digit number is 605.

Case 7: A = 7 In this case, the equation becomes: BC + 7C + B = 295

By trying different values for B and C, we can find that B = 0 and C = 4 satisfy the equation: 04 + 74 + 04 = 295

Therefore, when A = 7, the three-digit number is 704.

Case 8: A = 8 In this case, the equation becomes: BC + 8C + B = 295

By trying different values for B and C, we can find that B = 0 and C = 3 satisfy the equation: 03 + 83 + 03 = 295

Therefore, when A = 8, the three-digit number is 803.

Case 9: A = 9 In this case, the equation becomes: BC + 9C + B = 295

By trying different values for B and C, we can find that B = 0 and C = 2 satisfy the equation: 02 + 92 + 02 = 295

Therefore, when A = 9, the three-digit number is 902.

In conclusion, the three-digit number that the boy thought of is 159.

Answer 3

Solving the Problem

To solve this problem, we need to find a three-digit number that, when each of its digits is repeated three times, and then the first, second, and third digits are erased in the three repetitions, results in two two-digit numbers whose sum is 295.

Let's denote the three-digit number as abc. When each digit is repeated three times, we get abcabcabc. After erasing the first, second, and third digits in the three repetitions, we get the following two-digit numbers: - bc (erasing the first digit) - ac (erasing the second digit) - ab (erasing the third digit)

The sum of these two-digit numbers is 295.

Finding the Solution

Let's find the solution step by step: 1. We know that the sum of the two two-digit numbers is 295. 2. We also know that there are no zeros in the three-digit number.

Let's find the solution based on these constraints.

Solution

Let's denote the three-digit number as abc. After considering the constraints, the three-digit number that satisfies the given conditions is 853.

Therefore, the three-digit number that the boy thought of is 853.