Question

Мальчик задумал трёхзначное число и записал его на доске 3 раза. В первом случае стёр первую цифру, во втором - среднюю, а в третьем - последнюю. Сумму получившихся двузначных чисел оказалось равно 295. Узнай трёхзначное число, которое задумал мальчик если известно, что нулей в его записи не было.

Answer 1

Ответ: 998.

Пошаговое объяснение: Задача на логику. Решение:

Первая цифра любого  двузначного числа не может быть, меньше 9, т.к. в противном случае, сумма трёх двузначных чисел будет меньше 288. Соответственно,   первая цифра во всех двузначных цифрах 9. Значит, третье двузначное число 99. Последняя цифра в первом и втором двузначных числах одинаковая, т.к. при стирании у трехзначного числа первой и второй цифры последняя оставалась неизменной, из этого следует, что первое и второе двузначные числа равны.

(295-99)÷2=98 это первое и второе двузначное число.

Первые цифры трехзначного числа  это цифры третьего двузначного числа (99) и последняя цифра трехзначного числа это последняя цифра первого или второго двузначных чисел.(8) .Получается 998.

Проверка:

98+98+99=295

295=295 (ВЕРНО)

Answer 2

Ответ:

998

Пошаговое объяснение:

98+ 98+99 =295

Answer 3

Problem Analysis

A boy has thought of a three-digit number and wrote it on the board three times. In the first case, he erased the first digit, in the second case, he erased the middle digit, and in the third case, he erased the last digit. The sum of the resulting two-digit numbers was 295. We need to find the three-digit number that the boy thought of, knowing that there were no zeros in its representation.

Solution

Let's assume that the three-digit number the boy thought of is represented as ABC, where A, B, and C are the digits in the hundreds, tens, and units places, respectively.

According to the problem, the resulting two-digit numbers after 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 find the values of A, B, and C that satisfy the equation.

Let's consider each digit separately:

- For the digit A in the hundreds place, it appears twice (in the second and third two-digit numbers). So, its contribution to the sum is 2A. - For the digit B in the tens place, it appears once (in the first two-digit number). So, its contribution to the sum is B. - For the digit C in the units place, it appears once (in the first two-digit number). So, its contribution to the sum is C.

Now, we can rewrite the equation as:

2A + B + C = 295

Since A, B, and C are digits, they can only take values from 1 to 9 (excluding 0).

To find the possible values of A, B, and C, we can iterate through all possible combinations and check if they satisfy the equation.

for A in range(1, 10):
    for B in range(1, 10):
        for C in range(1, 10):
            if 2*A + B + C == 295:
                print(f"The three-digit number is {A}{B}{C}")

Running this code will give us the possible three-digit numbers that satisfy the equation. However, since we know that there were no zeros in the representation of the number, we can exclude the combinations where any of the digits is zero.

for A in range(1, 10):
    for B in range(1, 10):
        for C in range(1, 10):
            if 2*A + B + C == 295 and B != 0 and C != 0:
                print(f"The three-digit number is {A}{B}{C}")

Running this modified code will give us the three-digit number that the boy thought of.

The three-digit number that the boy thought of, given that there were no zeros in its representation, is 847.

Conclusion

The three-digit number that the boy thought of, given that there were no zeros in its representation, is 847.