Push Past The Putnam

(Stanford Putnam Training 2007)

There is a \(10\times 10\) board. Out of these 100, 9 cells are infected.

A cell becomes infected if it's adjacent to 2 already infected cells.

Think of the situation when the maximum number of cells are infected. How many cells remain uninfected then?

Challenge

Generalize for \(n\times n\) board with n-1 initially infected cells.

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