A beautiful question. Since we can't put more than one queen in the same row or column, with 100 queens on a 100*100 grid, there must be exactly one queen per row and per column. Assume for the sake of contradiction there are no queens in a particular 50*50 quadrant. Because there has to be one queen in each row and column, this forces 50 queens in each of the two adjacent quadrants, and zero queens in the diagonally opposite quadrant. Now consider that there must be only one queen per diagonal on the board. The two quadrants that each contain 50 queens share 99 diagonals on the board. That's a total of 100 queens on 99 diagonals, so there must be at least 2 queens on the same diagonal. Contradiction. Merlin