Question 85
A positive integer $n$ is stacked if $2 n$ has the same number of digits as $n$ and the digits of $2 n$ are multiples of the corresponding digits of $n$. For example, $1203$ is stacked because $2 \times 1203 = 2406$, and $2, 4, 0, 6$ are multiples of $1, 2, 0, 3$, respectively. Compute the number of stacked integers less than $1000$.