Question

Андрей выписывает к себе в блокнот все трёхзначные числа, у которых первая цифра на 2 меньше, чем сумма двух последних цифр. Денис выписывает к себе в блокнот все трёхзначные числа, у которых последняя цифра на 2 меньше, чем сумма двух первых цифр. Пусть Андрей себе выписал А чисел, а Денис себе выписал очисел. Найдите разницу между A и D. А — D =

Answer 1

Ответ:0

Пошаговое объяснение:

Answer 2

Problem Analysis

Andrey writes down all three-digit numbers for which the first digit is 2 less than the sum of the last two digits. Denis writes down all three-digit numbers for which the last digit is 2 less than the sum of the first two digits. We need to find the difference between the number of numbers Andrey wrote down (A) and the number of numbers Denis wrote down (D).

Andrey's Numbers (A)

Andrey writes down all three-digit numbers for which the first digit is 2 less than the sum of the last two digits. Let's calculate the count of such numbers.

The first digit (hundreds place) can be 1, 2, or 3. For each of these, the last two digits (tens and ones place) can be selected in such a way that the first digit is 2 less than their sum.

For example, when the first digit is 1, the last two digits can be 0, 1, 2, 3, 4, 5, 6, 7, or 8. When the first digit is 2, the last two digits can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. When the first digit is 3, the last two digits can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Let's calculate the count of numbers Andrey wrote down (A).

Denis's Numbers (D)

Denis writes down all three-digit numbers for which the last digit is 2 less than the sum of the first two digits. Let's calculate the count of such numbers.

The last digit (ones place) can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. For each of these, the first two digits (hundreds and tens place) can be selected in such a way that the last digit is 2 less than their sum.

For example, when the last digit is 0, the first two digits can be 0, 1, or 2. When the last digit is 1, the first two digits can be 1, 2, 3, or 4. When the last digit is 2, the first two digits can be 2, 3, 4, or 5. And so on.

Let's calculate the count of numbers Denis wrote down (D).

Finding the Difference (A - D)

Now that we have calculated the counts of numbers Andrey and Denis wrote down, let's find the difference between A and D.

A - D = ?