**Source:**AUSTMS Gazette 35

**Related Problem:**Pebble Placement Puzzle 1

**Problem:**Peggy aims to place pebbles on an n × n chessboard in the following way. She must place each pebble at the center of a square and no two pebbles can be in the same square. To keep it interesting, Peggy makes sure that no four pebbles form a non-degenerate parallelogram.

What is the maximum number of pebbles Peggy can place on the chessboard?