I know that a four-digit palindrome must have the same first and last digit, and the same second and third digit. So, the first digit can be any of the nine nonzero digits, from 1 to 9. The second digit can be any of the ten digits, from 0 to 9. The third and fourth digits are determined by the first and second digits, respectively. Therefore, the number of four-digit palindromes is 9 times 10, or 90. 
A palindrome is a number that reads the same forwards and backwards, such as 3003. How many positive four-digit integers are palindromes?