Question

Сколько существует четырехзначных чисел не делящихся на 1000 у которых первая и последняя цифра не четная?

Answer 1

Всего четырёхзначных чисел, у которых первая и последняя цифра чётные 4*10*10*5=2000.
Из них делящихся на 1000  4*1*1*1=4
Всего чисел подходящих под условие равно  2000-4=1996

Answer 2

Number of Four-Digit Numbers Not Divisible by 1000 with First and Last Digits Not Even

To find the number of four-digit numbers not divisible by 1000 with the first and last digits not even, we can break it down into the following steps:

1. Total Number of Four-Digit Numbers: - There are 9000 four-digit numbers in total (from 1000 to 9999).

2. Numbers Divisible by 1000: - The numbers divisible by 1000 are those that end with three zeros. - Therefore, the total number of numbers divisible by 1000 is 9 (1000, 2000, 3000, ..., 9000).

3. Numbers with Even First and Last Digits: - The first and last digits can be even (0, 2, 4, 6, 8). - Therefore, the total number of numbers with even first and last digits is 5 * 5 = 25 (0, 2, 4, 6, 8 for the first digit and 0, 2, 4, 6, 8 for the last digit).

4. Numbers Not Divisible by 1000 with First and Last Digits Not Even: - Subtract the numbers divisible by 1000 and the numbers with even first and last digits from the total number of four-digit numbers.

Calculation

- Total four-digit numbers: 9000 - Numbers divisible by 1000: 9 - Numbers with even first and last digits: 25 - Numbers not divisible by 1000 with first and last digits not even: 9000 - 9 - 25 = 8976

Therefore, there are 8976 four-digit numbers not divisible by 1000 with the first and last digits not even.