A positive integer k is called a "lucky" number if the units digit of k^6 is 4. How many lucky numbers smaller than 1000 are there?
I think it is 1 because there is only one possible value which is 2.
$k^6\equiv 4\pmod{10}$ has solutions $k\equiv \pm 2\pmod{10}$.
So $2,8,12,18,22,28, ...$ all work.
+600 
