Hint: The lowest route contains more 2's than the highest route.
Answer: Highest = 24. Lowest = 12.
You are given a 10x10x10 cube composed of one thousand 1x1x1 mini-cubes glued together.
If you removed the outermost layer, how many mini-cubes would you have removed?
Hint: Think about one face at a time.
You started with 10x10x10 = 1000 cubes.
Removing the outermost layer would leave a 8x8x8 large cube = 512 cubes.
Therefore you would have removed 488 cubes (1000 - 512 = 488).