There are 900 six-digit palindromes that are divisible by 11.
A six-digit palindrome has the form ABC CBA, where A, B, and C are digits. A cannot be zero because then it wouldn't be a six-digit number. So A can be any digit from 1 to 9, and B and C can be any digit from 0 to 9.
A number is divisible by 11 if the alternating sum of its digits is divisible by 11. For the palindrome ABC CBA, the alternating sum of the digits is A - B + C - C + B - A = 0. Since 0 is divisible by 11, every six-digit palindrome is divisible by 11.
Since A can be any of the 9 digits from 1 to 9, and B and C can each be any of the 10 digits from 0 to 9, there are 9 10 10 = 900 possible six-digit palindromes. Since all of these are divisible by 11, there are 900 six-digit palindromes divisible by 11.
