OMCPLP 2012 Problem 2

Maria has a board of size $n \times n$ , initially with all the houses painted white. Maria decides to paint black some houses on the board, forming a mosaic, as shown in the figure below, as follows: she paints black all the houses from the edge of the board, and then leaves white the houses that have not yet been painted. Then she paints the houses on the edge of the next remaining board again black, and so on. a) Determine a value of $n$ so that the number of black houses equals $200$ . b) Determine the smallest value of $n$ so that the number of black houses is greater than $2012$ .

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