5. How many five-digit numbers of the form $\overline{a b 16 c}$ are divisible by 16? $(a, b, c-$ arbitrary digits, not necessarily different).

ANSWER: 90.
Solution: Note that the first digit does not affect divisibility, hence, a=1,..,9. On the other hand, divisibility by 8 implies that c=0 or 8. If c=0, then $b$ must be even, and if $c=8$ - odd. In both cases, we get 5 options, from which the total number is $9 *(5+5)=90$.