1. The squares of a chessboard are numbered from left to right and top to bottom (so that the first row reads $1,2, \ldots, 8$, the second reads $9,10, \ldots, 16$, and so forth). The number 1 is on a black square. How many black squares contain odd numbers?
Solution: 16. The black squares in the $n$th row contain odd numbers when $n$ is odd and even numbers when $n$ is even; thus there are four rows where the black squares contain odd numbers, and each such row contributes four black squares.