1. Place $1,2, \cdots, n$ on a circle such that the absolute difference between any two adjacent numbers is 3, 4, or 5. Find the smallest $n$ that allows such an arrangement.
1. $n<6$, since $1,2,3$ cannot be adjacent, at this point there are at most two other numbers, which cannot separate $1,2,3$, so it is impossible to place them. $n=6$, $1,2,3$ cannot be adjacent, $4,5,6$ can only be placed with one interval each, but 4 cannot be adjacent to 2,3, which is impossible. $n=7$ is possible, as shown in Figure 5-7, so the smallest $n$ is 7.