Problem 393
Migrating ants
An n×n grid of squares contains n2 ants, one ant per square.
All ants decide to move simultaneously to an adjacent square (usually 4 possibilities, except for ants on the edge of the grid or at the corners).
We define f(n) to be the number of ways this can happen without any ants ending on the same square and without any two ants crossing the same edge between two squares.
You are given that f(4) = 88.
Find f(10).
蚂蚁迁徙
在n×n的方形网格上有n2只蚂蚁，每个方格上一只。
所有的蚂蚁决定同时移动到相邻的方格上（通常有4种可能，除非蚂蚁在网格的边上或角上）。
若没有两只蚂蚁在移动后落到同一方格或是移动时穿过了同一条边，记这样的移动方式总数为f(n)。
已知f(4) = 88。
求f(10)。