+983 There are two methods to do this problem.
Method 1: Pattern Finding
There are 9 palindromes with 2 digits
There are 90 palindromes with 3 digits
There are 90 palindromes with 4 digits
There are 900 palindromes with 5 digits
So 1 digit: 9
2 digits: 9
3 digits: 90
4 digits: 90
5 digits: 900
6 digits: 900
7 digits: 9000
9000
Method 2: Counting
The 7 digit palindrome is in this format:
ABCDCBA
There are 9 choices for A
10 for B
10 for C
10 for D
\(9\cdot{10}\cdot{10}\cdot{10}=\boxed{9000}\)
I hope this helped,
Gavin
