Posted by the Guardian, could become too popular, I don't know. This is a small variation of the problem.
There is a rectangular 100x100 grid of cells in a dish. Some of them are infected with a virus. An infected cell stays infected forever. A healthy cell gets infected if at least two of its neighbors are infected. What is the minimal starting number of infected cells to infect the whole 100x100 grid?
Required mathematics knowledge: nothing beyond basic logic.
Wait with this problem. While playing around with the integer side length problem, I found an issue that applies here as well.
I have a pretty convincing argument, but not a full proof that you need
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