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Found problems: 1

2011 AIME Problems, 14
Tags: AIME , 2011 AIME II
There are $N$ permutations $(a_1,a_2,\dots,a_{30})$ of $1,2,\dots,30$ such that for $m\in\{2,3,5\}$, $m$ divides $a_{n+m}-a_n$ for all integers $n$ with $1\leq n <n+m\leq 30$. Find the remainder when $N$ is divided by 1000.