Let me first re-phrase your question: What is the number of (positive) integers less than 10000 (5 digits) and greater than 999 (3 digits)?
The greatest 4 digit integer would be 9999.
The greatest 3 digit integer would be 999.
Let's do some subtraction: 9999 - 999 = 9000
This works because as we count up from 999, each positive integer encountered satisfies your requirements until reaching 10000.
The lowest positive 4-digit number is 1000
-22
There are one thousand. Starting at 2000 and going to 2999
-48
5*5*4*4 = 400
The smallest, positive 4-digit multiple of 17 is 1,003.
The lowest positive 4-digit number is 1000
There are 294 such numbers.
18 positive integers and 36 integers (negative and positive)
4,000 even numbers, 4,000 odd numbers.
-22
90
I believe there are 2 positive three-digit perfect cube numbers, that are even.
1
-2
There are 200 positive four digit integers that have 1 as their first digit and 2 or 5 as their last digit. There are 9000 positive four digit numbers, 1000 through 9999. 1000 of them have 1 as the first digit, 1000 through 1999. 200 of them have 2 or 5 as their last digit, 1002, 1005, 1012, 1015, ... 1992, and 1995.
900 This explains it. A positive integer is a palindrome if it reads the same forward and backwards such as 1287821 and 4554. Determine the number of 5-digit positive integers which are NOT palindromes. We start by counting the total number of 5 digit positive integers. The first digit is between 1 and 9, so we have 9 choices. Each of the other 4 digits can be anything at all (10 choices for each). This gives us 9(10)4 = 90000 five-digit positive integers. Now we need to count the number of 5 digit palindromes. Again, we have 9 choices for the first digit and 10 choices for each of the next two. The tens and units digits however are fixed by our choices so far. Therefore, there are only 900 five-digit palindromes. Therefore, the total number of five-digit positive integers which are not palindromes is 90000-900 = 89100.