I'm trying to find out the number of 7 digit numbers that are palindromes. My method is this (don't laugh):
If the correct number is 9000, what am I doing wrong? All wrong?
There is a one-to-one correspondence between 4-digit numbers and 7-digit palindromes.
There is a one-to-one correspondence between 5-digit numbers and 10-digit palindromes.
If n is even, there is a one-to-one correspondence between n-digit numbers and (2n-1)-digit palindromes.
If n is odd, there is a one-to-one correspondence between n-digit numbers and (2n)-digit palindromes.
Wasn't trying to sound like a jerk, I just wasn't sure what you were getting at at first.
I get the idea, though, that you just have to consider the first 4 digits and the first can't be a 0.
The first time round I was trying to do that: Find the number of selections of 4 without repetition that don't start with 0, and then add the number of selections with 4 repetitions, 3 repetitions, and 2 repetitons. My method was a bit ridiculous though (new to this).