Question 1
Lucas paints the entire outside of a cube blue. He then saws the cube into $27$ equally sized cubes. He neatly stacks these $27$ cubes so that he gets a tower of $27 \times 1 \times 1$ cubes.
At most how many of the $110$ side faces of cubes on the outside of his tower are blue?
At most how many of the $110$ side faces of cubes on the outside of his tower are blue?