Question

A sealed rectangular box measuring 8 x 6 x 18 contains 864 sugar cubes, each measuring 1 x 1 x 1. How many sugar cubes are touching the box?

Answer 1

I hate these

Answer 2

8x6x18 = 864, so all the sugarcubes on the outside are touching. that's:
8 x 6 = 48 for each end (96 total)
8 x 16 = 128 for top and bottom (minus the ones we already counted for the ends) (256 total)
4 x 16 = 64 for left and right sides (minus the ones we already counted for ends and top and bottom) (128 total)

Grand total is 480

Answer 3

Thank you! But where did the 16 come from?

Answer 4

find the number of cubes not touching the walls: 6x4x16 and subtract that from total

Answer 5

notice when you count the left side in my drawing, you are already counting one row of the top, bottom, front, and back. So after counting the sides, the length you have to count for other sides is length-2. that being said, danil's path to the answer (which arrives at teh same number) is more elegant. :-)