There are as many palindromic 12-bit binary strings as there are permutations with repetition of 6-bit binary strings, which is equal to [tex]2^6=64[/tex].
There are also only two permutations with repetition of 6-bit binary strings, that when each of them is mirrored and the result is "glued" to the right side of the original string, will give a palindromic string without 10 as a substring.
Those strings are 000000 and 111111.
Therefore there are [tex]64-2=62[/tex] palindromic 12-bit binary strings with 10 as substring.
