Solution to Warm-up Puzzle:
As this figure shows, for most blocks, a pedestrian can walk from a corner across the street to a corner of the neighboring building.
The two blocks marked with 2 require walking through two buildings to travel to one another. For example, to go from (1,0) to (2,0), go to the northeast corner of (1,0), cross to (1,1), then go diagonally to the southeast corner of (1,1), and then cross the plowed street to the northeast corner of (2,1). From there go to the southwest corner of (2,1) and then into the block (2,2).