Question 8
For a permutation $p = (a_1, a_2, \ldots, a_9)$ of the digits $1,$ $2,$ $\ldots,$ $9,$ let $s(p)$ denote the sum of the three $3$-digit numbers $a_1a_2a_3,$ $a_4a_5a_6,$ and $a_7a_8a_9.$ Let $m$ be the minimum value of $s(p)$ subject to the condition that the units digit of $s(p)$ is $0.$ Let $n$ denote the number of permutations $p$ with $s(p) = m.$ Find $|m - n|.$