+612 How many sequences of 6 digits $x_1, x_2, \ldots, x_6$ can we form, given the condition that no two adjacent $x_i$ have the same parity? Leading zeroes are allowed. (Parity means 'odd' or 'even'; so, for example, $x_2$ and $x_3$ cannot both be odd or both be even.)
Regardless of whether 
is odd or even, we have 5 choices for 
: if is odd then must be one of the 5 even digits, otherwise if is even then must be one of the 5 odd digits. Similarly, we then have 5 choices for 
, 5 choices for 
, and so on.
Since can be any of the 10 digits, the answer is 
