3. Find all two-digit numbers of the form $\overline{X Y}$, if the number with a six-digit decimal representation $\overline{64 X 72 Y}$ is divisible by 72.
Answer: $80,98$.

Solution. Since $\overline{64 X 72 Y}$ is divisible by 8, then $Y \in\{0,8\}$, and since $\overline{64 X 72 Y}$ is divisible by 9, then $6+4+X+7+2+Y=19+X+Y$ is a multiple of 9. If $Y=0$, then $X=8$, and if $Y=8$, then either $X=0$ (cannot be the first digit of the number), or $X=9$. Therefore, the desired two-digit numbers are $\overline{X Y}=80$ and $\overline{X Y}=98$.