points with integer coordinates. To start with, there are no trees at all. The foresters plant

the first tree at (0; 0). Each year, they carry out tree planting according to the following

rule. If there is a tree on the point (m; n) but there are no trees on the points (m+1; n) and

(m; n + 1), then they can choose to remove the tree on (m; n) and plant new trees on the

points (m; n + 1) and (m + 1; n).

For an integer k >= 1, the kth diagonal consists of all points (m; n) with m + n = k - 1. Is

it possible for the foresters to arrange their planting so that eventually there are no trees on

the first 2 diagonals? What about the first 3 diagonals? 4 diagonals? Can you generalize?