## Problem of the Day #400: Squirrel CityApril 22, 2012

Posted by Saketh in : potd , trackback

In Squirrel City there is a $100$ by $100$ grid on which every treehouse is located, one at each lattice point. The administration is doing some construction and needs to chop down trees for wood.

They know that no citizen will complain unless there exists a treehouse from which at least two different stumps can be observed. Furthermore, there must be at least one treehouse left for the squirrels to use.

Determine the greatest number of trees which can be chopped down without inciting any complaints. Assume that the radius of each tree is negligible when compared to the gaps between the trees.