# USACO 2020 Gold December Contest, Replication

In the problem Replication, in the problem statement, it says that every hour all the robots will move either north, south, east, or west. I got stuck on this part for a bit thinking that even once the center of the mass of robots got a place, they couldn’t just stop and keep replicating, they had to keep moving. However, in the solution, it says to observe that once we have reached a possible center-spot, we can stay and keep replicating from that spot until a robot hits the border. This contradicts the problem statement, which said the bots move every hour. Am I mistaken in this? I just want to make sure I interpret problems correctly in the future, because to me, when it says the swarm of robots move every hour in some direction means they cannot stay in place.

Thanks!

You can move in one direction and then revert that move during the next timestep, which has the same effect.

Oh snap, I just realized that would actually work. I was assuming that there would be a case where you move, replicate, and there wouldn’t be space to move back or something like that, but that would only be true if you cannot replicate more anyway.

Thanks!