21. Pablo's teacher has given him 27 identical white cubes. She asks him to paint some of the faces of these cubes grey and then stack the cubes so that they appear as shown. What is the largest possible number of the individual white cubes which Pablo can leave with no faces painted grey?
A 8
B 12
C 14
D 15
E 16
Solution
D We can see 19 of the 27 cubes. Of these there are 12 which we can see have at least one grey face. The remaining cubes could have all their faces white. So the maximum number of cubes that could be all white is $27-12=15$.