Question 73
Consider a $4\times4$ square grid. Two distinct cells sharing a side are called neighbors. Initially every cell is red; later a cell may change color, being either red or blue. Performing an operation on a cell $c$ means simultaneously changing the color of $c$ and all its neighbors (red becomes blue and blue becomes red).
Find all values of $n$ for which there is a set of $n$ distinct cells such that performing an operation on each of them makes the whole grid blue.
Find all values of $n$ for which there is a set of $n$ distinct cells such that performing an operation on each of them makes the whole grid blue.