Question 12
A square $(2n+1)\times(2n+1)$ chessboard, with $n\gt 0$, is colored so that each square is white or black. A square is called special if at least $n$ other squares in its row and at least $n$ other squares in its column have the same color as it.
a. Prove that there are at least $2n+1$ special squares.
b. Give an example with at most $4n$ special squares.
c. Determine, as a function of $n$, the minimum possible number of special squares.
a. Prove that there are at least $2n+1$ special squares.
b. Give an example with at most $4n$ special squares.
c. Determine, as a function of $n$, the minimum possible number of special squares.