Maximum number of pieces that can be placed in a 4x4 board

GRE Quant Problem Solving
1

O O O O
O O O O
O O O O
O O O O

The figure above is a 4×4 board used for a certain game. What is the maximum number of squares where a game piece can be placed so that there are no other pieces in the horizontal, vertical, or diagonal path of another piece?

Is there an analytical way to solve this?

2

0 0 1 0
1 0 0 0
0 0 0 1
0 1 0 0

This is known as the 8-Queens problem or the N-queens problem.