How many palindromes below 10000 (i.e. between 0 and 9999 inclusively) are not divisible by 11?
List them.
A number is divisible by 11 if and only if the sum of its odd-numbered digits (1st digit, 3rd digit, 5th digit, etc.) minus the sum of its odd-numbered digits are divisible by 11. Thus, all palindromes with an even number of digits are divisible by 11. Thus, we must only consider palindromes with an odd number of digits.
All 10 one-digit numbers ( 0, 1, ... 8, 9) qualify.
Also, all 90 of the 3 digit palindromes except:
121
242
363
484
616
737
858
979
In other words, 10 + 90 - 8 = 92. Too many for me to list.
Just counting (spoiler)
