Originally Posted by

**onemachine** The way I understand it is that a square is a square if it has 4 unique sides. When the squirrels move one position to the left or right, there are 4 new unique sides created (and thus, a second, unique square). However, when they move positions 9 times, they have created the same square they started with. When they move to the 10th time, they are creating the same square they made after the first position. The squirrels can create equivalent squares while rotating throught the positions around the square. Thus, I believe the answer to part A is 36!/4, because the equivalence class of the original square has 4 elements, of which only one is a unique square.

I'm hoping someone can convince me that this is either correct or incorrect...