Virus on a grid

One hundred computers are connected in a 10x10 network grid. At the start exactly nine of them are infected with a virus. The virus spreads like this: if any computer is directly connected to at least 2 infected neighbours, it will also become infected. Will the virus infect all 100 computers?

The image shows a possible example of the initial infection. You can try to fill it in to see if ultimately the network will consist of 100 orange dots. But the question is not asking what happens to this example. I want to know what will happen given any initial configuration of infected computers.

Published in The Guardian by Alex Bellos.

Solution