I believe the answer is actually 4. Here's my reasoning:

Ok so you take the square root of 120 which is around 10.954

If you times that by 4 (the 4 equal sides of the square plot of land) = 43.82 (rounded up)

Then divide that by 12 = 3.65

So technically, only 3 posts would be needed to keep them 12 feet apart. However, in order for the fence to be held up around the perimeter, you'd need at least 4 posts.

I wonder if anyone else has a take on this though?