by-n grid where some squares hold a number or a pencil tip that is pointed in one of the
cardinal directions. The goal is to draw 'pencils' that partition the squares of the grid. Each
pencil occupies 2k+ 1 squares for some k≥ 1. A k-pencil has a horizontal or vertical body of
length k, a tip pointing away from one end of the body, and a lead that is a path of k squares
starting from the tip. In addition, any number inside a body must match the body's size. We …