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There are 90 palindromic numbers between 100 and 1000
As 20569.8 is not palindromic, any number that is like it must contain that property and similarly be non-palindromic, so no.
That would be 26 . . . its square is 676.There are two smaller palindromic squares . . . 121 and 484 ... but they're the squares of11 and 22 respectively, which are palindromic, so they flunk the question's specifications.
There are more 12-digit palindromic numbers than 11-digit palindromic numbers. This is because the number of possible 12-digit palindromic numbers is greater than the number of possible 11-digit palindromic numbers. In general, the number of palindromic numbers of length n is 9 * 10^((n-1)/2), so for 11-digit palindromic numbers, there are 9 * 10^5 = 900,000 possibilities, while for 12-digit palindromic numbers, there are 9 * 10^6 = 9,000,000 possibilities.