-1000
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For the 3 digit numbers from 900 - 999 then the 1st and 3rd numbers must be 9. The middle digit can vary from 0 - 9 making 10 palindromes in this range.
For the 4 digit numbers from 1000 to 1900 then the 1st and thus the 4th digit can only be 1. The middle pair of digits must be identical and can vary from 00 to 88 making 9 palindromes in this range.
Note : 1991 is outside the permitted range.
In total there are thus 10 + 9 = 19 palindromes between 900 - 1900.
The palindromic numbers between 900 and 1900 are:909919929939949959969979989999100111111221133114411551166117711881This is a total of 19 numbers.
There are 900 6-digit palindromes.
1900
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.
1-digit: 9 2-digit: 9 3-digit: 9 x 10 = 90 4-digit: 9 x 10 = 90 5-digit: 9 x 10 x 10 = 900 6-digit: 9 x 10 x 10 = 900